Exaleiphō (ἐξαλείφω) means to wipe out completely — to blot, erase, obliterate. From ex (out) + aleiphō (to anoint, smear). The word appears in Acts 3:19 (sins blotted out), Revelation 3:5 (names not erased from Book of Life), Revelation 7:17; 21:4 (God wiping tears).
Exaleiphō is used for two theologically opposite divine actions: blotting out sin (the debt record erased) and wiping away tears (the pain record erased). Acts 3:19: "Repent and turn to God, so that your sins may be wiped out [exaleiphō]." Colossians 2:14: God "canceled the charge of our legal indebtedness, which stood against us... nailing it to the cross." Revelation 21:4: "He will wipe every tear [exaleiphō] from their eyes." The same divine eraser removes both the record of sin and the record of suffering. Both acts are grace.
Exaleiphō literally applies to wiping a wax tablet clean — the ancient equivalent of formatting a hard drive. Debt records, tears, names: all are written things that can be erased. The Book of Life is the ultimate register; to have one's name not erased from it is the ultimate security. Revelation 3:5's negative construction ("I will never blot out") is a powerful promise: the overcomer's name is permanently inscribed.