The most common and most likely answer to this crossword clue is the 3 plus 3 plus 4 letter word TOP AND TAIL
I've seen this crossword clue in Independent
T
O
P
A
N
D
T
A
I
L
More clues leading to the result TOP AND TAIL
Buddy explains!
The straight part
We know that "Cut off bits of fruit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cut off bits of fruit = top and tail.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.