The most common and most likely answer to this crossword clue is the 7 letter word SNUBBED
I've seen this crossword clue in Financial Times
S
N
U
B
B
E
D
Buddy explains!

The straight part
We know that "Cut" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cut = snubbed.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SNUBBED mean?
SNUBBED verb- To slight, ignore or behave coldly toward someone.
- To turn down; to dismiss.
- To check; to reprimand.
- To stub out (a cigarette etc).
- To halt the movement of a rope etc by turning it about a cleat or bollard etc; to secure a vessel in this manner.
- To clip or break off the end of; to check or stunt the growth of.
- To sob with convulsions.