If you are looking for synonyms for the phrase "gives heave-ho", you may consider using words like dismiss, fire, oust, eject, remove, expel, banish, or even kick out. All of these words indicate a forceful action of removing someone or something from a position or role. They can be used interchangeably with the phrase "gives heave-ho" in a variety of contexts, ranging from personal relationships to business dealings. Regardless of the specific word choice, the underlying meaning remains the same: moving on from a situation or person.