take up vs mop up

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

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

As verbs, mop up is a hyponym of take up; that is, mop up is a word with a more specific, narrower meaning than take up:

Other hyponyms of take up include mop, wipe up, blot, sponge up.

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

take up (verb)	mop up (verb)
pursue or resume	finish a task completely
return to a previous location or condition	defeat thoroughly
adopt	to wash or wipe with or as if with a mop
take up as if with a sponge
take out or up with or as if with a scoop
accept
take in, also metaphorically
take up a liquid or a gas either by adsorption or by absorption
occupy or take on
take up and practice as one's own
begin work or acting in a certain capacity, office or job
turn one's interest to
take up time or space