There are several synonyms for the term "breaking off" which imply the act of putting an end to something. "Terminating" implies ending something permanently or abruptly. "Cancelling" and "nullifying" imply the act of putting an end to an agreement or contract. "Discontinuing" implies the act of stopping something that has been going on for some time. "Halting" implies stopping something that is in progress temporarily. "Ending" and "concluding" refer to the act of bringing something to a close, and "abandoning" implies the act of giving up something that was previously pursued. These synonyms can be used interchangeably, depending on the context and the situation.