The most common and most likely answer to this crossword clue is the 6 letter word EXCISE
I've seen this crossword clue in The Guardian
E
X
C
I
S
E
Buddy explains!

The straight part
We know that "cut out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cut out = excise.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 EXCISE mean?
EXCISE noun- A tax charged on goods produced within the country (as opposed to customs duties, charged on goods from outside the country).
- To impose an excise tax on something.
- To cut out; to remove.