The phrase "sign off on" implies approval or authorization of a particular task or document. Some antonyms for "sign off on" include: reject, disapprove, veto, and deny. Reject means to refuse to accept or consider something. Disapprove denotes a negative judgment or evaluation. Veto means to prohibit or block a decision. Deny suggests a refusal to acknowledge or admit something. Other possible antonyms for "sign off on" include dissent, refute, renounce, and disown. These words all convey the opposite meaning of "sign off on" by indicating opposition, disagreement, or contradiction.