clear up vs mop up

clear up is not a noun while mop up is a noun.

Word	Noun	Adjective	Verb	Adverb
clear up	No	No	Yes	No
mop up	Yes	No	Yes	No

As verbs, clear up and mop up are synonyms defined as:

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

clear up (noun)	mop up (noun)
	a concluding action

clear up (verb)	mop up (verb)
free (the throat) by making a rasping sound	finish a task completely
finish a task completely	defeat thoroughly
make free from confusion or ambiguity; make clear	to wash or wipe with or as if with a mop
make clear and (more) comprehensible
become clear