break up vs cut in

break up and cut in both are verbs.

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

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

break up (verb)	cut in (verb)
laugh unrestrainedly	interrupt a dancing couple in order to take one of them as one's own partner
break or cause to break into pieces	mix in with cutting motions
come to an end	break into a conversation
separate (substances) into constituent elements or parts	drive in front of another vehicle leaving too little space for that vehicle to maneuver comfortably
cause to go into a solution	allow someone to have a share or profit
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