How does Christ take away our sins? It's a process. Our sins are removed through a gradual life process of resisting harm and doing good.
"The next day John saw Jesus coming toward him, and said, “Behold! The Lamb of God who takes away the sin of the world!" (John 1:29)
"'To believe in the Lord's name' signifies to live according to the commandments of His teaching; ... 'the Lord's name" signifies all things by which He is worshiped, thus all things of love and faith." (Emanuel Swedenborg, Apocalypse Explained 295:13)