In the Greek text, note that verses 8-11 are a single sentence.

Note that this next section is all an expansion of the last word in the previous verse "God". Paul simply cannot resist the opportunity to enlarge upon the gospel of God and what He did in providing salvation for man.

Steven Cole has a poignant introduction in his exposition of this passage observing that...

Most evangelistic appeals today pitch the gospel as the way to have an abundant life. “Jesus came to offer you abundant life. Trust in Him and He will give you peace, joy, and a truly happy life.” While all of those claims are true if properly defined, what the salesman hasn’t told the potential customer is that your problems may grow much worse after you have trusted in Christ.

When we pitch Jesus as a better way to self-fulfillment, we’re promoting an Americanized message that is not identical with the biblical gospel. What if the potential convert is from a Muslim background? Will his life be one of trouble-free happiness if he trusts in Christ? His family will disown him and possibly kill him because he converted to Christianity. What if he is from China? He may lose his job or be sent to a labor camp on account of his Christian faith. In 2 Timothy 3:12 (note), Paul says,

“Indeed, all who desire to live godly in Christ Jesus will be persecuted.”

We had better present a gospel that is worth suffering for!

In the Greek text, verses 8-11 are a single sentence. In verse 8, Paul exhorts Timothy not to

“be ashamed of the testimony of our Lord, or of me His prisoner, but join with me in suffering for the gospel according to the power of God.”

Then in 1:12, Paul states,

“For this reason, I also suffer these things, but I am not ashamed.”

So our text is sandwiched between an exhortation to embrace suffering for the gospel without shame and an example of one who had done so. The motive that Paul uses to urge Timothy to embrace suffering is the glorious gospel of God’s sovereign grace. He is saying that…

Because God has saved us by His sovereign grace, we should be willing to suffer for the gospel.

Getting a grasp of the glorious truth that God saved us according to His own purpose and grace, which was granted to us in Christ Jesus from all eternity, will give us the strength to endure suffering for the sake of the gospel. Remember, these words are coming to us from the Holy Spirit through the mouth of a man who is facing imminent execution on account of the gospel. So these truths are powerfully practical, but we must understand and submit to them in order to benefit from them. (Why Suffer for the Gospel? )

Saved (4982) (sozo) (Click word study of sozo) has the basic meanings of to rescue from peril, danger or destruction, to protect, to keep alive including preserving one's life in either a physical or spiritual sense.

Sozo occurs 54x in the Gospels, 14 uses relating to deliverance from disease or demon possession (Mt 9:21-21, Lu8:36), 20x to the rescue of physical life from some impending peril or death (Mt 8:25; 14:30) and the remaining 20x referring to spiritual salvation (Mt1:21; 10:22; Lu 8:12; Jn10:9). Below you will see a table with links to all 108 NT uses.

Saved is in the aorist tense (as is the verb "called" below) which refers to God's act of saving (and calling) the believer at a point in time. It recalls a specific historical event.

Do you remember the day you were saved? (I only know the season myself). Paul’s is saying that since God has saved us and called us at a definite point of time, this truth ought to strengthen our faith to continue on unashamedly in the face of opposition knowing we have God's gifts (v7) and power to overcome.

Spurgeon writes that

Believers in Christ Jesus are saved. They are not looked upon as persons who are in a hopeful state, and may ultimately be saved, but they are already saved. Salvation is not a blessing to be enjoyed upon the dying bed, and to be sung of in a future state above, but a matter to be obtained, received, promised, and enjoyed now. The Christian is perfectly saved in God’s purpose; God has ordained him unto salvation, and that purpose is complete. He is saved also as to the price which has been paid for him: “It is finished” was the cry of the Saviour ere he died. The believer is also perfectly saved in his covenant head, for as he fell in Adam, so he lives in Christ. This complete salvation is accompanied by a holy calling. Those whom the Saviour saved upon the cross are in due time effectually called by the power of God the Holy Spirit unto holiness: they leave their sins; they endeavour to be like Christ; they choose holiness, not out of any compulsion, but from the stress of a new nature, which leads them to rejoice in holiness just as naturally as aforetime they delighted in sin. God neither chose them nor called them because they were holy, but he called them that they might be holy, and holiness is the beauty produced by his workmanship in them. The excellencies which we see in a believer are as much the work of God as the atonement itself. Thus is brought out very sweetly the fulness of the grace of God. Salvation must be of grace, because the Lord is the author of it: and what motive but grace could move him to save the guilty? Salvation must be of grace, because the Lord works in such a manner that our righteousness is for ever excluded. Such is the believer’s privilege—a present salvation; such is the evidence that he is called to it—a holy life. (Morning and Evening)

Steven Cole  has a good discussion on salvation writing...

As I’ve often said, salvation is a radical word. You don’t need saving if you’re in pretty good shape. All you need then is a little help. You need saving when you’re perishing and are helpless to save yourself. The Bible uses a number of metaphors to show that we are desperately helpless and unable to save ourselves. It says that we were dead in our sins (Eph. 2:1; John 11). It pictures us as blind (John 9; 2 Cor. 4:4), lost (Luke 15), leprous (Luke 5:12-14), crippled (Luke 5:18-25), deaf (Mark 7:31-35), and hardened in our hearts (Eph. 4:18). Salvation means that God came to us while we were His sinful enemies (Rom. 5:8, 10), rescued us from our helpless condition, and gave us new life as His free gift. As William Hendriksen put it (New Testament Commentary, 1 & 2 Timothy, Titus [Baker], p. 232), “God has delivered us from the greatest of all evils and he has placed us in possession of the greatest of all blessings.”

But here is where much controversy arises. Many will say, “It’s true that God saves us, but the sinner has to exercise his free will in order to accept God’s gift.” In other words, God has done His part by sending Christ to die for our sins, but now it’s up to us to accept Him. Implicit in this teaching is that everyone has the ability to believe in Christ. Without such ability, they say, God’s offer of salvation is a sham. What good is it to tell a sinner to trust in Christ if he is not able to trust in Christ?

Several things need to be said here. First, sinners must repent and trust in Christ to be saved. Christ commands sinners to repent and believe the gospel (Mark 1:15). But the command does not imply ability. Jesus plainly said (John 6:44, 65), “No one can come to Me unless the Father who sent Me draws him; and I will raise him up on the last day…. For this reason I have said to you, that no one can come to Me unless it has been granted him from the Father.” Clearly, the Father does not draw everyone to Christ, because Jesus promises to raise up on the last day all who come to Him through the Father’s drawing. But not all will be saved. Jesus said (Luke 10:22), “All things have been handed over to Me by My Father, and no one knows who the Son is except the Father, and who the Father is except the Son, and anyone to whom the Son wills to reveal Him.” Clearly, Jesus does not will to reveal the Father to everyone. When the disciples asked Jesus why He spoke to the multitudes in parables, He replied (Matt. 13:11), “To you it has been granted to know the mysteries of the kingdom of heaven, but to them it has not been granted.”

In John 8:43, 44, Jesus asked the unbelieving Jews, “Why do you not understand what I am saying? It is because you cannot hear My word. You are of your father the devil, and you want to do the desires of your father….” Jesus did not say, “It is because you chose by your free will not to hear My word,” but rather, “because you cannot hear My word.” Because they were not born again, they were of their father the devil, and they acted in accordance with their nature.

If we had time, I could multiply verses that say the same thing (e.g., Rom. 8:7-8; 1 Cor. 2:14; 2 Cor. 4:4; Eph. 2:1-3; 4:17-18). So to speak of “free will” is really misleading. As Martin Luther correctly argued against Erasmus (The Bondage of the Will), the fallen human will (before conversion) is in bondage to sin. Or, as Charles Wesley put it (“And Can it Be?”), “Long my imprisoned spirit lay, fast bound in sin and nature’s night….” God has to send that quickening (life-giving) ray to awaken us from our darkness, death, and bondage. At that instant, we respond in faith and repentance, which also come from God. It is God who saves us. (Why Suffer for the Gospel?)

AND CALLED US: kai kalesantos (AAPMSG):

Called (2564) (kaleo) has several nuances including (1) to identify by name or attribute, call, call by name, name (Lu 1:59, Jn 10:3) (2) to request the presence of someone at a social gathering, invite (Mt 22:9) (3) to use authority to have a person or group appear or to summon (Mt 2:7) and (4) from the meanings ‘summon’ & ‘invite’ there develops the extended sense of to choose for receipt of a special benefit or experience which is the meaning in the context of the present verse (Heb 5:4 of God calling one to be priest, 1Pe 5:10 called to eternal glory).

Vincent comments that called

It is Paul’s technical term for God’s summoning men to salvation.

Jamieson rightly says

The call comes wholly from God and claims us wholly for God. (and adds that) “Holy” implies the separation of believers from the rest of the world unto God.

As John Gill says

The calling here spoken of is not to an office, nor a mere call by the external ministry of the word, but a call by special grace, to special privileges, to grace and glory; and is an high and heavenly one, and is here called holy.

WITH A HOLY CALLING: klesei hagia: (Ro 8:28ff; 9:24; 1Th 4:7; 2 Th 2:13,14; Heb 3:1; 1Pet 2:9; 2:21)

A holy calling - A set apart calling. A sanctified calling. The calling is holy and the result of the calling is to be holiness in those called.

Or as Paul says...

God has not called us for the purpose of impurity (uncleanness, word used of graves), but in sanctification (holiness, "to dedicate ourselves to the most thorough purity" [Amp]). (1 Thes 4:7, NASB)

Moses describes what God's will is for His people...

'For I am the LORD your God. Consecrate yourselves therefore, and be holy; for I am holy. And you shall not make yourselves unclean with any of the swarming things that swarm on the earth. (Leviticus 11:44)

Matthew Poole comments on a holy calling noting that...

in order to our obtaining it, hath effectually called, renewed, and sanctified us.

Holy (40) (hagios) (Click study on hagios).   We are to be set apart (hagios) from sin and set apart to the Savior. (Click discussion of Be holy and holiness)

The holy calling is from God and is often referred to as His effectual call of a sinner to salvation in which the sinner called, willingly accepts the salvation God offers him. This is  God’s invitation to man to accept the benefits of salvation. In short, in the epistles, God's calling always denotes an effective and successful calling.

Why is it referred to as a holy calling? Gill has this succinct answer:

The Author of it is holy; it is a call to holiness, and the means of it are holy; and in it persons have principles of grace and holiness implanted in them; and are influenced to live holy lives and conversations." Stated another way this calling is holy because it is not only the invitation to a holy life, but also to the holy life which the one called is expected to live. God has always desired His people to be a "set apart" people (Dt 7:6, Isa 52:11).

Holiness is not an option for the believer, it is a family obligation (see how His "children" are to act see note 1 Peter 1:15; 1:16) for all those who are joined together in Christ and all "who name the name of the Lord (are to) abstain (aorist imperative - do it now, sense of urgency)  from wickedness." (see note 2 Timothy 2:19, see Torrey's Topic "Character of Saints")

The Christian’s holy calling is described in some detail in Ephesians 1–3, especially Eph 1:3-14 where we see the truths that saints are chosen (see note Ephesians 1:4), predestined (see notes Ephesians 1:5, 1:11), adopted as sons (see note Ephesians 1:5), accepted in the Beloved (see note Ephesians 1:6), redeemed through His blood (see note Ephesians 1:7), forgiven (see note Ephesians 1:7), sealed with the Holy Spirit (see note Ephesians 1:13) and given the earnest of our inheritance (see note Ephesians 1:14).

In addition to a holy calling, saints also have a high ("upward") calling (see note Philippians 3:14) and a heavenly calling  (see note Hebrews 3:1)

Hiebert comments on the two words saved and called writing that...

"The order of the two terms, united under one article, is interesting. Boise observes 'As the order now stands, it presents the picture of one who is wandering away from God. He is stopped in his course. This first divine act saves him. He is then called, invited, with a holy calling-holy in contrast with the invitations to sin such as he had previously listened to. The calling is the work of God's holiness and it leads to holiness in the called.'" (2 Timothy by D. Edmond Hiebert).

Steven Cole notes that...

One common objection to the view that salvation is totally by God’s grace is that such teaching will lead to licentiousness. The charge was leveled against Paul (see notes Romans 3:8; 6:1). But he always made it clear that God calls us to live holy lives. If someone claims to be saved but continues living in sin, he had better examine whether he was truly saved at all. Salvation that does not result in a life of progressive holiness is not genuine salvation. It dishonors the name of God when someone claims to be saved, especially someone in public ministry, but he lives in sin. While no one can be totally free from sin in this life, those whom God has saved will sin less as they grow in holiness in thought, word, and deed. God’s call to holiness is effectual, which is to say, it is something that He purposes and promises to accomplish in us. Yet at the same time, we must actively strive for holiness according to the means that God has provided. (Why Suffer for the Gospel? )

NOT ACCORDING TO OUR WORKS: ou kata ta erga hemon:  (Titus 3:5, Eph 2:8-9,10, Ro 3:20, 4:5, 11:6; Gal 2:16 ) (Click discussion of good deeds Torrey's Good Works)

Not according to - Fittingly Paul uses the strongest Greek word for "not" (ou) to convey that there is absolutely no way works of a man can merit salvation. This false belief is so important to refute that he reiterates this same idea many times in his epistles...

Romans 3:20 (note) because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin.

Romans 4:4 (note)  Now to the one who works, his wage is not reckoned as a favor, but as what is due. 4:5 But to the one who does not work, but believes in Him who justifies the ungodly, his faith is reckoned as righteousness,

Romans 11:6 (note) But if it is by grace, it is no longer on the basis of works, otherwise grace is no longer grace.

Galatians 2:16 nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, that we may be justified by faith in Christ, and not by the works of the Law; since by the works of the Law shall no flesh be justified.

Ephesians 2:8 (note) For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; 2:9 not as a result of works, that no one should boast. 2:10 For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.

Titus 3:4 (note) But when the kindness of God our Savior and His love for mankind appeared, 3:5 He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit, 3:6 whom He poured out upon us richly through Jesus Christ our Savior,

Our works have not the least trace of holiness to merit God's holy calling. As Spurgeon once said...

The first link between my soul and Christ is not my goodness but my badness, not my merit but my misery, not my riches but my need.

Saints were saved not according to their "good" works (none are good, no not one) but for or unto good works (see notes Ephesians 2:10; Titus 2:14; Hebrews 10:24; 1 Peter 2:12; Revelation 22:12) (cf Acts 9:36 ,1Ti 6:18, Rev 22:12) the "ultimate" work being to bring glory to our Father in heaven.

Our righteous deeds are but "filthy rags" (Isa 64:6) and the only thing our lives truly merit is the wrath of Almighty God. Thus Paul always emphasizes that men are saved despite what they deserve, not because of what they deserve!

Gill explains man's "works" as "not properly good works (see notes 2 Timothy 2:21; 2 Timothy 3:17), being destitute of faith in Christ, and proceeding neither from a right principle, nor to a right end"...no matter how "good" they may appear to other men. (Jer 17:9,10) Salvation is not earned nor merited by anything that the sinner does. Isaac Watts hymn says it so well...

Alas and did my Savior bleed? and did my Sovereign die?
Would He devote that sacred head for such as worm as I?
Was it for crimes that I have done He groaned upon the tree?
Amazing pity! grace unknown! and love beyond degree!
Click to play & ponder the full hymn @ Cyberhymnal

Calvin astutely observes that

If God chose us before the creation of the world He could not have considered the question of our works, which could have had no existence at a period when we ourselves were not.

John Blanchard quips...

We are saved not by merit but by mercy.

Spurgeon

William Wickham being appointed by King Edward to build a stately church, wrote in the windows, "This work made William Wickham." When charged by the king for assuming the honour of that work to himself as the author, whereas he was only the overseer, he answered that he meant not that he made the work, but that the work made him, having before been very poor, and then in great credit.

Lord, when we read in thy Word that we must work out our own salvation, thy meaning is not that our salvation should be the effect of our work, but our work the evidence of our salvation.— Feathers for Arrows

BUT ACCORDING TO HIS OWN PURPOSE: alla kata idian prothesin: (Dt 7:7, 7:8; Isa 14:26,27; Mt 11:25,26; Lu 10:21; Ro 8:28; Ep 1:9, 1:11)

But according to - This is a humbling contrast of which we would be wise to never lose sight. He did not save us because of how famous we were, of how great we were, on the basis of what great things we had done, etc, but because it was His holy purpose! This is humbling and should stimulate great gratitude.

Jamieson adds that..

The origination of salvation was of His own purpose, flowing from His own goodness, not for works of ours coming first, but wholly because of His own gratuitous, electing love

His own - This phrase is emphatic in the Greek sentence. God was self-moved, impelled by motives, not from without, but from within Himself and "His own private purpose" (Wuest translation).

Hiebert adds that...

Only God's sovereign and wise purpose is the norm for our salvation. If our salvation depended on our own deserving, we might well despair, but it has its ground in God's eternal and unshakable purpose. And that purpose expressed itself in "grace," the unmerited favor of God toward us guilty sinners." (2 Timothy by D. Edmond Hiebert).

Purpose (4286