cut up vs damage

cut up is not a noun while damage is a noun.

Word	Noun	Adjective	Verb	Adverb
cut up	No	Yes	Yes	No
damage	Yes	No	Yes	No

As verbs, damage is a hypernym of cut up; that is, damage is a word with a broader meaning than cut up:

cut up (noun)	damage (noun)
	the act of damaging something or someone
	any harm or injury resulting from a violation of a legal right
	the occurrence of a change for the worse
	loss of military equipment
	the amount of money needed to purchase something

cut up (adjective)	damage (adjective)
cut into pieces

cut up (verb)	damage (verb)
significantly cut up a manuscript	inflict damage upon
separate into isolated compartments or categories	suffer or be susceptible to damage
damage or injure severely
cut to pieces