When it comes to finding synonyms for the phrase "shove away", there are quite a few options to choose from. Some possible alternatives include "push away", "thrust aside", "rebuff", "reject", "brush off", "dismiss", "repel", "ignore", "deflect", "divert", "send packing", and "turn aside". Each of these words carries slightly different connotations, so it's important to choose the one that best fits the context of your sentence or conversation. No matter which word you choose, though, the basic idea is the same: you're pushing something or someone away from you in a forceful or decisive way.