“Sorry to cut you off.”
Cut someone off means to interrupt them. Sorry to cut you off. politely acknowledges an interruption, often when time is short and the speaker needs the main point.
B1-02 / CEFR B1 / EPISODE 02
Keeping a work conversation on track
SceneIt's late at night in the office. Frank and his coworker, Priya, are racing to meet a deadline for an important client. The pizza arrived an hour ago.

WORDS & CONTEXT
Cut someone off means to interrupt them. Sorry to cut you off. politely acknowledges an interruption, often when time is short and the speaker needs the main point.
Let me just finish that thought. reclaims the floor after an interruption. That thought is the idea left unfinished, and just suggests it will take only a moment, softening the request.
Here Good luck with that. is mildly exasperated irony, rather than sincere encouragement. It lightly challenges Frank's claim that the printer fears him. The phrase can also be sincere; tone and context distinguish the meanings.
Earn means to receive something through effort or deserve it. You've earned it. encourages someone to accept a reward. Priya gives Frank the last pizza after his work late into the night.