The Bible does not use the phrase "forgive and forget" though it is often used in society. Depending on what one means by "forgive and forget," the phrase has some biblical support.
Is 'forgive and forget' a biblical concept?
The Bible certainly instructs us to forgive one another (e.g., Matthew 6:14; Ephesians 4:32). In fact, we are to forgive others as God has forgiven us (Matthew 6:12), even when someone sins against us many times (Matthew 18:22). And unwillingness to forgive someone hinders one's fellowship with God (Matthew 6:15).
God says when He forgives that He "forgets" ("will not remember") our sins (Isaiah 43:25). While God is all-knowing and does not literally forget anything, the idea is that He no longer holds against us sins He has forgiven. We cannot simply decide to "forget" sins or erase them from our memory. In fact, in some cases it would be unwise or unsafe to do so.
Instead, when we forgive someone who has sinned against us, we choose to no longer hold the sin against them. We do not hold a grudge or seek revenge. But in some cases, we may need to no longer associate with a person or use precautions for safety reasons. We can choose to forgive while also not foolishly restoring trust to an unrepentant sinner.
Forgiving others who have sinned against us is a sign of spiritual maturity. Colossians 3:12–13 teaches, "Put on then, as God's chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience, bearing with one another and, if one has a complaint against another, forgiving each other; as the Lord has forgiven you, so you also must forgive."
The way we forgive others should reflect how Christ has forgiven us: "Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you" (Ephesians 4:32). How has Christ forgiven us? Completely and unconditionally. However, the forgiveness He offered was not easy. It came at the cost of His life on the cross for our sins.
Forgiving others also allows us to move forward in our own Christian life. Though not specifically talking about forgiveness, the words of Philippians 3:13–14 are helpful to consider, "Brothers, I do not consider that I have made it my own. But one thing I do: forgetting what lies behind and straining forward to what lies ahead, I press on toward the goal for the prize of the upward call of God in Christ Jesus." We do not "forget" the sin, but we choose not to focus on past sin and press ahead to live God's calling for our lives, choosing to live for His glory. When we do, we show the example of Jesus and can greatly impact the lives of other people.
Why should we forgive?
How can I extend forgiveness to those who sin against me?
If we sin against someone, do we need to confess to them?
Does the Bible talk about forgiving yourself?
How do I receive forgiveness from God?
Truth about the Christian Life