The phrase "signs off on" refers to the act of giving approval or authorization to something. Antonyms for this phrase could include words such as disapprove, reject, veto, or decline. When someone signs off on a document or agreement, they are essentially indicating that they agree with its contents and are allowing it to move forward. However, if they were to use one of the antonyms listed above, they would be communicating that they do not agree with what is being proposed and are not willing to give their approval. It is important to carefully consider the implications of signing off on any document or decision before doing so.