cut off vs break up

cut off is an adjective but break up is not an adjective.

Word	Noun	Adjective	Verb	Adverb
cut off	No	Yes	Yes	No
break up	No	No	Yes	No

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

Other hypernyms of cut off include cut off, disrupt, interrupt.

As verbs, cut off and break up are synonyms defined as:

Other synonyms of cut off include disrupt, interrupt.

cut off (adjective)	break up (adjective)
detached by cutting

cut off (verb)	break up (verb)
cease, stop	laugh unrestrainedly
make a break in	break or cause to break into pieces
remove by or as if by cutting	come to an end
remove surgically	separate (substances) into constituent elements or parts
break a small piece off from	cause to go into a solution
cut off and stop	cause to separate
	close at the end of a session
	bring the association of to an end or cause to break up
	make a break in
	set or keep apart
	break violently or noisily; smash
	attack with or as if with a pickaxe of ice or rocky ground, for example
	release ice
	destroy the completeness of a set of related items
	take apart into its constituent pieces
	suffer a nervous breakdown
	disband
	to cause to separate and go in different directions
	discontinue an association or relation; go different ways