Paul also uses this idea of "delivering unto Satan" in 1 Corinthians 5:5, where he says concerning the man who had his father's wife:
... deliver such a one unto Satan for the destruction of the flesh, that the spirit may be saved in the day of the Lord Jesus.
-- 1 Corinthians 5:5 (KJV)
It is clear to me that "delivering someone unto Satan" involves the church completely severing fellowship with him/her, i.e. "Purge out therefore the old leaven" (v. 7), "I wrote unto you in an epistle not to company with fornicators" (v. 9), "But now I have written unto you not to keep company, if any man that is called a brother be a fornicator ..." (v. 11)
The purpose of doing this is to quarantine the person so that his/her sin does not infect the entire church. While cut off from fellowship, the person has an opportunity to weigh up the benefit of fellowship versus the benefit of persisting with their transgression. If they choose to abandon their sin, then they are free to repent of it, seek forgiveness for it, and return into fellowship with the church.
Such a practice can only be effective if the entire church is of ONE MIND. Five times in the book of Deuteronomy God says through Moses concerning judgment, "thine eye shall have no pity ..." (Deuteronomy 7:16, 13:8, 19:13, 19:21, 25:12). If there is any pity shown by the church for the one quarantined, then it will be impossible for that person to distinguish a life with fellowship from a life without it. The choice must be COMPLETELY left to the one who is quarantined.
Forgiveness must be available, because it is foundational to the Gospel, but it should only be given if it is sought. Jesus says (emphasis mine),
3Take heed to: If thy brother trespass against thee, rebuke him; and if he repent, forgive him. 4 And if he trespass against thee seven times in a day, and seven times in a day turn again to thee, saying, I repent; thou shalt forgive him.
-- Luke 17:3-4 (KJV)
Jesus is sovereign in the church (Ephesians 1:22, Colossians 1:18), and Satan is sovereign in the world (John 12:31, 14:30, 16:11). Being cut off from the church, immediately places the sinner outside of the kingdom of heaven, and back into the kingdom of this world, from whence he/she came.
Those who sin must be given to opportunity to decide where they prefer to be, with Jesus, or without.
Paul was a blasphemer, and he lived his life without Christ in the kingdom of this world, being moved about by the ruler of this world. He was one of those whom Jesus foretold would appear:
They shall put you out of the synagogues: yea, the time cometh, that whosoever killeth you will think that he doeth God service.
-- John 16:2 (KJV)
However, Paul repented of his sin, and chose a life with Jesus above life without him.
7 But what things were gain to me, those I counted loss for Christ. 8 Yea doubtless, and I count all things but loss for the excellency of the knowledge of Christ Jesus my Lord: for whom I have suffered the loss of all things, and do count them but dung, that I may win Christ, 9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: 10 That I may know him, and the power of his resurrection, and the fellowship of his sufferings, being made conformable unto his death;
-- Philippians 3:7-10 (KJV)