polish off vs mop up

polish off is not a noun while mop up is a noun.

Word	Noun	Adjective	Verb	Adverb
polish off	No	No	Yes	No
mop up	Yes	No	Yes	No

As verbs, polish off and mop up are synonyms defined as:

Other synonyms of polish off include clear up, finish off, finish up, get through, wrap up.

polish off (noun)	mop up (noun)
	a concluding action

polish off (verb)	mop up (verb)
finish a task completely	finish a task completely
finish eating all the food on one's plate or on the table	defeat thoroughly
kill intentionally and with premeditation	to wash or wipe with or as if with a mop