The most common and most likely answer to this crossword clue is the 8 letter word CASTRATE
I've seen this crossword clue in Financial Times
C
A
S
T
R
A
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More clues leading to the result CASTRATE
Buddy explains!

The straight part
We know that "to perform a delicate operation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to perform a delicate operation = castrate.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 CASTRATE mean?
CASTRATE noun- A castrated man; a eunuch.
- To remove the testicles of an animal.
- To remove the ovaries and/or uterus of an animal.
- To take something from; to render imperfect or ineffectual.