Real Dictionary

cut in
phrasal verb: If you cut in on someone, you interrupt them when they are speaking.

cut in in American English
to move in suddenly, as into a small opening in a lane of traffic
to move or thrust oneself, a vehicle, etc., abruptly between others

cut in in British English
to break in or interrupt
noun: a separate shot or scene inserted at a relevant point

cut-in in American English
something that is cut in, as a close-up of some object inserted into a film sequence
noun: a still, as of a scene or an object, inserted in a film and interrupting the action or continuity