In Acts 22:16, Ananias says to Paul, “Now why do you delay? Get up and be baptized, and wash away your sins, calling on His name.” Our sins are forgiven by calling on the name of Jesus; that is, putting our trust in Him. The removal of our sin is presented as being washed way during baptism.
In Ezekiel 37:23 God declares
They will no longer defile themselves with their idols, or with their detestable things, or with any of their transgressions; but I will deliver them from all their dwelling places in which they have sinned, and will cleanse them. And they will be My people, and I will be their God.
They will be cleansed of their sins by God. Similarly, in Jeremiah 33:8 God says,
I will cleanse them from all their iniquity by which they have sinned against Me, and I will pardon all their iniquities by which they have sinned against Me and by which they have transgressed against Me.
Here the cleansing is a result of being pardoned by God. Jeremiah 50:20 speaks of a time when a search will be made to find Israel’s iniquity, but none will be found because God will pardon the remnant that remains. God’s pardon renders the iniquity such that it cannot be found and used to condemn a person. In Isaiah 38:17 “For You have cast all my sins behind Your back” is understood as the sins are pardoned.
1 John 1:7 tells us “the blood of Jesus His Son cleanses us from all sin” when we walk in harmony with the Lord. We are cleansed of our sin. The blood of Jesus shed on the cross is the cleansing agent, but only for those who walk in the light. John 3:16-21 has more on our interaction with the Light. 1 John 1:8 confirms Romans 3:23 “for all 1ahave sinned and fall short of the glory of God” by saying we deceive ourselves when we deny our sins. The heart of these three verses is found in 1 John 1:9. Facing our sins instead of denying they exist, that is “if we confess our sins,” God will “forgive us our sins” because of His faithfulness and righteousness. His forgiveness results in our cleansing from them.
In Psalm 32:1 “transgression is forgiven.” The next phrase repeats the same thought with, “Whose sin is covered.” Therefore, forgiveness of a transgression is equated with the covering of sin. Psalm 32:1 is also quoted in the New Testament in Romans 4:7. We see the same equating of forgiveness and covering in Psalm 85:2, “You forgave the iniquity of Your people; You covered all their sin. Selah.” Sin and iniquity are parallel words used for repetition and forgiveness is again equated with the covering of sin. When a sinner find salvation, a multitude of sins are covered. (James 5:20)
Speaking of a New covenant Jeremiah 31:34 says, “… for I will forgive their iniquity, and their sin I will remember no more.” Again, our sins are forgiven. This time however the sins are forgotten and remembered no more.
Probably the most familiar one comes from Micah 7:19, “He will again have compassion on us; He will tread our iniquities under foot. Yes, You will cast all their sins Into the depths of the sea.” To tread them under foot is to subdue them. They lose their power overs us. Casting them into the sea renders them lost forever. Washed, cleansed, forgiven, forgotten, or cast into the sea they will never be held against us again.
One method of forgetting sin that likely come from record keeping is found in Acts 3:19. Peter uses the phrase “wiped away” to illustrate what happens to our sins when we repent and return to God. Perhaps He is thinking of wiping away wet ink before it dries or possibly rubbing the papyrus until the ink is gone.
Similarly, the Old Testament uses the phrase “blot out.” But it is often used of blotting out people or their memory. It is also used in prayers to for one’s own transgressions to be forgotten or for those of another person to not be forgotten. Psalms 69:28 goes further to say, “May they be blotted out of the book of life And may they not be recorded with the righteous.” Though the blotting out of sins is sought in the Old Testament it is not said to be done.
Paul borrows an image from first century business practices in Colossians 2:13-14 where he speaks of our transgressions against God represented as a “certificate of debt consisting of decrees against us.”
When you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions, having canceled out the certificate of debt consisting of decrees against us, which was hostile to us; and He has taken it out of the way, having nailed it to the cross.
Here our sin is simply “taken out of the way.” It has been nailed to the Cross where Jesus paid the debt on our behalf. Also, in 1 John 3:5 sins are taken away.
Best of all though is to not commit sin in the first place. Having love for one another go a long was toward avoiding sin. 1 Peter 4:8 “Above all, keep fervent in your love for one another, because love covers a multitude of sins.”
All scripture quotations are from NASB95
 1 Kings 13:34, 2 Kings 14:27, Psalms 9:5, 69:28, 109:13
 Nehemiah 4:5, Psalms 51:1, 51:9, Psalm 109:14, Jerimiah 18:23