The most common and most likely answer to this crossword clue is the 4 letter word MOWN
I've seen this crossword clue in The Daily Telegraph
M
O
W
N
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 = mown.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 MOWN mean?
MOWN verb- To cut down grass or crops.
- To cut down or slaughter in great numbers.