These are my Bible study notes on the topic of circumcision.

Circumcision began with Abraham as a physical act, and continued for the nation of Israel. But even in the Pentateuch, the first five books of the Bible, there are numerous indications that circumcision was symbolic of a spiritual state. The Israelites were exhorted to be "circumcised in heart".

In the New Testament, the spiritual symbolism of circumcision is emphasised, and transcends the physical. Circumcision was an important and contentious doctrinal issue in the early New Testament church, as the early Jewish Christians contended with the question of how non-Jewish (or non-Israelite) people could come to salvation through Jesus Christ.

Old Testament

Genesis 17:10-14,23-27 Covenant with Abraham and his descendants forever. v11 says circumcision is a sign of the covenant. Acts 7:8 calls it the "covenant of circumcision". In Genesis 17, note the repetition of the phrase "male child", implying it was intended to be done on a person when they're a child. Consider that in light of the debate about adult circumcision.
Genesis 21:4 Isaac was circumcised on the 8th day.
Genesis 34:13-25 Simeon and Levi convinced the men of Shechem to be circumcised, and then killed them, due to Shechem's treatment of Dinah.
Exodus 4:24-26 Moses set upon by the Lord, apparently for failing to circumcise his son.
Exodus 6:12,30 Moses uses "uncircumcision" of his lips as a metaphor (for what?).
Exodus 12:43-49 Circumcision is necessary to keep the Passover. A stranger may partake of the Passover once all the family is circumcised.
Leviticus 12:2-4 Circumcise a son on the eighth day.
Leviticus 19:23 When Israel went into the promised land, they were to regard the fruit of the trees as "uncircumcised" for several years, before being allowed to eat it.
Leviticus 26:41; Deuteronomy 10:16; 30:6-8 Metaphor for having a heart open to God. Deuteronomy 29:4
Joshua 5:2-9 The Israelite males who were born in the wilderness hadn't been circumcised, and so had to be circumcised before they entered the promised land. Jeremiah 4:4,14 Circumcision of the heart.
Jeremiah 6:10 Judah's ears are uncircumcised, and they can't give heed.
Jeremiah 9:25-26 God said He would punish the uncircumcised nations, and circumcised (Israel) also, because Israel was really uncircumcised in heart.
Ezekiel 44:9 Circumcision of both heart and flesh will be expected in the Millennial temple, for Israelites and foreigners who wish to go into the temple.

Pejorative "Uncircumcised"

Genesis 17:14 God would reject someone physically uncircumcised.
Genesis 34:14 Dinah's brothers said it would be a shame for her to marry someone uncircumcised.
Exodus 6:12,30 Moses said he is of "uncircumcised lips" to mean he couldn't speak well.
Joshua 14:3 Samson's parents told him not to take a wife from among the "uncircumcised Philistines".
1 Samuel 14:6 Jonathan talking to his armour-bearer about the Philistines.
1 Samuel 17:26,36 David describing Goliath.
1 Samuel 31:4; 1 Chronicles 10:4 Saul describing the Philistines, who he was afraid would torture him. Thus he fell on his sword.
2 Samuel 1:20 Referring to the Philistines, in David's song of mourning for Saul and his sons.
Isaiah 52:1 "the uncircumcised and the unclean"

New Testament

Luke 1:59 Infant John the Baptist was circumcised on the 8th day.
Luke 2:21 Infant Jesus was circumcised on the 8th day.
John 7:22-23 Jesus uses the circumcision law as a point of discussion about Sabbath-keeping.
Acts 15 Jerusalem conference. The essential question is about whether the newly called Gentiles must be circumcised or not (see v.5).
Acts 16:3 Paul circumcised Timothy because the Jews knew his father was Greek. Compare with Titus in Galatians 2:3.
Acts 21:21 Rumours that Paul was teaching "all the Jews who are among the Gentiles to forsake Moses, saying that they ought not to circumcise their children nor to walk according to the customs."
Romans 2:25-29 Circumcision inwardly, of the heart.
Romans 3:1 What advantage has the Jew? What is the profit of circumcision?
Romans 4:9-12 Abraham father of circumcised and uncircumcised, with the faith he had while still uncircumcised.
1 Corinthians 7:17-20 Remain as you were when called, circ or uncirc. Circ is nothing; uncirc is nothing; keeping the commandments is what matters.
Galatians 2:3 Not even Titus, being Greek, was compelled to be circumcised (yet Paul circumcised Timothy in Acts 16:3 — why? Timothy was half Jewish, while Titus was Gentile).
Galatians 5:1-6 Don't become entangled in a yoke of bondage. If you become circumcised, Christ will profit you nothing, and you're indebted to keep the whole law.
Galatians 5:6 In Christ Jesus neither circumcision nor uncircumcision avails anything, but faith working through love.
Galatians 6:15 For in Christ Jesus neither circumcision nor uncircumcision avails anything, but a new creation. Philippians 3:2-7 Beware of dogs, evil workers, "the mutilation"! For we are the circumcision, who worship God in the Spirit, rejoice in Christ Jesus, and have no confidence in the flesh... Paul was well-qualified as one of Israel by physical reckoning (circumcision, ancestry, having the law), but his hope was really in Christ.
Colossians 2:11-15 In Christ we were circumcised with the circumcision made without hands. This also talks about baptism and the metaphor of death and burial of the old man, and raising of a new man with Christ.
Colossians 3:10-11 Putting on the new man is what's important, not Greek/Jew, circ./uncirc. etc.

Spiritual Metaphor Greater Than Physical Act

Philippians 3:3,7-9
Colossians 2:11-13

Metonym for Being a Jew

Galatians in particular uses "circumcision" as a way to refer to Jews and contrast them with Gentiles.

See my notes on "Law and Grace—Understanding Galatians" which examines the issue in Galatians.

Acts 10:45; 11:2
Romans 3:1,29-30; 4:12; 15:8
Galatians 2:3,7-9 Circumcision is a key issue. "Yet not even Titus who was with me, being a Greek, was compelled to be circumcised." which is the first mention of circumcision in Galatians, but in the context of discussion about "a different gospel" and Judaism.
Galatians 2:3-4 Issue described as liberty of Christ versus bondage that is somehow connected with circumcision.
Galatians 2:7-9,12-15; 5:1-6; 6:12-15 It appears that "circumcision" is connected with the "Gentile" issue. "Circumcised" are Jews, "uncircumcised" are Gentiles. Circumcision is not just an action, but an intimate part of the Judaic identity that sets them apart from Gentiles. Romans 4:12; Galatians 2:12; Ephesians 2:11-12; Colossians 4:11 refer to those who are "of the circumcision", apparently to mean the Jews. Romans 3:1-2; 15:8 appears to use circumcision as a metonym for being a Jew. Romans 2:28-29 says that circumcision of the heart is what is truly important.
Galatians 3:28-29 There is neither Jew nor Greek... all in Christ are Abraham's spiritual descendants and children of the promise.
Galatians 5:1-6 is talking about circumcision, in the context of attempting justification by law. Specifically in connection with the "bondage" of the old covenant from Sinai. Galatians 5:2 puts circumcision at odds with Christ.
Galatians 5:11 Pro-circumcision people find the message of the cross offensive, and persecute those who preach Christ.
Philippians 3:3 and Colossians 2:11 emphasise the spiritual body of metaphorically circumcised people.
Colossians 2:13 talks about the "uncircumcision of your flesh", talking to the Gentile audience and contrasting their physical uncircumcision with the spiritual circumcision that they receive through the Holy Spirit.

Spiritual Symbolism

Leviticus 26:41; Deuteronomy 10:16; 30:6-8 Metaphor for having a heart open to God. Deuteronomy 29:4
Joshua 5:9 Circumcision "rolled away the reproach of Egypt" for the Israelites.
Jeremiah 4:4 Circumcision of the heart.
Jeremiah 6:10 Uncircumcised ears.
Jeremiah 9:25-26 God said He would punish circumcised (Israel) along with the uncircumcised nations, because Israel was really uncircumcised in heart.
Ezekiel 44:9 Circumcision of both heart and flesh will be expected in the Millennial temple, for Israelites and foreigners who wish to go into the temple.
Romans 2:25-29 Circumcision of the heart.
Philippians 3:2-3 For we are the circumcision, who worship God in the Spirit, rejoice in Christ Jesus, and have no confidence in the flesh...
Colossians 2:11 In Christ we were circumcised with the circumcision made without hands.