The most common and most likely answer to this crossword clue is the 5 letter word CORER
I've seen this crossword clue in The Times
C
O
R
E
R
More clues leading to the result CORER
- Gosh! I'm not sure what steals Jonathan's heart?
- This has a disheartening effect on apples, for example
- Utensil initially cuts out rubbish, emptying russet?
- One provides seedless apples for cooking
- Company’s router losing out — it may be disheartening for Apple
- It's surprising I don't know what leaves eater gutted
Buddy explains!

The straight part
We know that "what leaves eater gutted" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what leaves eater gutted = corer.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.