mix in vs cut in

mix in and cut in both are verbs.

Word	Noun	Adjective	Verb	Adverb
mix in	No	No	Yes	No
cut in	No	No	Yes	No

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

mix in (verb)	cut in (verb)
cause (something) to be mixed with (something else)	interrupt a dancing couple in order to take one of them as one's own partner
add as an additional element or part	mix in with cutting motions
	break into a conversation
	drive in front of another vehicle leaving too little space for that vehicle to maneuver comfortably
	allow someone to have a share or profit