The most common and most likely answer to this crossword clue is the 4 letter word MOWS
I've seen this crossword clue in The Guardian
M
O
W
S
Buddy explains!

The straight part
We know that "Cuts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cuts = mows.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 MOWS mean?
MOWS noun- A gull, seagull.
- A prison, or other place of confinement.
- A hiding place; a secret store or den.
- A breeding-cage for birds.
- A cage for hawks, especially while moulting.
- (in the plural) A building or set of buildings where moulting birds are kept.
- The crying sound of a cat; a meow, especially of a kitten.
- The crying sound of a gull.
- An exclamation of disapproval; a boo.
- The act of mowing (a garden, grass etc.)
- A shot played with a sweeping or scythe-like motion.
- To cut down grass or crops.
- To cut down or slaughter in great numbers.
- A scornful grimace; a wry face.
- To make grimaces, mock.
- A stack of hay, corn, beans or a barn for the storage of hay, corn, beans.
- The place in a barn where hay or grain in the sheaf is stowed.
- To put into mows.