The most common and most likely answer to this crossword clue is the 6 letter word WOUNDS
I've seen this crossword clue in The Guardian
W
O
U
N
D
S
Buddy explains!

The straight part
We know that "Cuts, perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cuts, perhaps = wounds.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 WOUNDS mean?
WOUNDS 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).