break up vs cut off

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

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

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

Other synonyms of break up include disrupt, interrupt.

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

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

break up (verb)	cut off (verb)
laugh unrestrainedly	cease, stop
break or cause to break into pieces	make a break in
come to an end	remove by or as if by cutting
separate (substances) into constituent elements or parts	remove surgically
cause to go into a solution	break a small piece off from
cause to separate	cut off and stop
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