The most common and most likely answer to this crossword clue is the 5 letter word WOUND
I've seen this crossword clue in The Daily Telegraph
W
O
U
N
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 = wound.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 WOUND mean?
WOUND noun- An injury, such as a cut, stab, or tear, to a (usually external) part of the body.
- A hurt to a person's feelings, reputation, prospects, etc.
- An injury to a person by which the skin is divided or its continuity broken.
- To hurt or injure (someone) by cutting, piercing, or tearing the skin.
- To hurt (a person's feelings).
- To blow air through a wind instrument or horn to make a sound.
- To cause (someone) to become breathless, as by a blow to the abdomen, or by physical exertion, running, etc.
- To cause a baby to bring up wind by patting its back after being fed.
- To turn a boat or ship around, so that the wind strikes it on the opposite side.
- To expose to the wind; to winnow; to ventilate.
- To perceive or follow by scent.
- To rest (a horse, etc.) in order to allow the breath to be recovered; to breathe.
- To turn a windmill so that its sails face into the wind.
- To turn coils of (a cord or something similar) around something.
- To tighten the spring of a clockwork mechanism such as that of a clock.
- To entwist; to enfold; to encircle.
- To travel in a way that is not straight.
- To have complete control over; to turn and bend at one's pleasure; to vary or alter or will; to regulate; to govern.
- To introduce by insinuation; to insinuate.
- To cover or surround with something coiled about.
- To cause to move by exerting a winding force; to haul or hoist, as by a winch.
- To turn (a ship) around, end for end.