The most common and most likely answer to this crossword clue is the 3 letter word HEW
I've seen this crossword clue in Financial Times
H
E
W
Buddy explains!

The straight part
We know that "Cut down" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cut down = hew.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 HEW mean?
HEW verb- To chop away at; to whittle down; to mow down.
- To shape; to form.
- To act according to, to conform to; usually construed with to.
- Hue; colour
- Shape; form
- Destruction by cutting down.