mop up vs polish off

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

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

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

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

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

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