divide vs cut up

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

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

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

divide (noun)	cut up (noun)
a ridge of land that separates two adjacent river systems
a serious disagreement between two groups of people (typically producing tension or hostility)

divide (adjective)	cut up (adjective)
	cut into pieces

divide (verb)	cut up (verb)
perform a division	significantly cut up a manuscript
move or break apart	separate into isolated compartments or categories
force, take, or pull apart	damage or injure severely
make a division or separation	cut to pieces
separate into parts or portions
act as a barrier between; stand between