The most common and most likely answer to this crossword clue is the 8 letter word FLAT-TOP
I've seen this crossword clue in The Guardian
F
L
A
T
-
T
O
P
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 = flat-top.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 FLAT-TOP mean?
FLAT-TOP noun- A short haircut in which the hair is brushed straight up then cut flat across the top.
- An aircraft carrier.
- A type of stringed instrument, most often an acoustic guitar, with a flat top (as opposed to an archtop), with strings held in place with pins, and with a complex system of bracing struts on the top.