Synonyms for Polish off:

n.

overcome, defeat, beat, crush, thrash, overpower, knock out, smash, win. manage, try, ingest, touch, have, taste. polish off (noun)
finish off, finish up, slay, clear up, HIT, wrap up, finish, bump off, get through, eat up, mop up, remove, dispatch.

v.

use up (verb)
dispatch, finish off, finish up, eat up.

Other synonyms:

Other relevant words:
beat, thrash, manage, smash, crush, defeat, dispatch, overpower.