Synonyms for Polish Off (same or very similar meaning)
WordNet sense 1 (kill intentionally and with premeditation):
dispatch, hit, murder, off, remove, slay, bump offWordNet sense 2 (finish eating all the food on one's plate or on the table):
finish, eat upWordNet sense 3 (finish a task completely):
clear up, get through, finish up, finish off, mop up, wrap upFrom the ODE community, based on WordNetadd/edit