damage vs cut up

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

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

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

damage (noun)	cut up (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

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

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