The most common and most likely answer to this crossword clue is the 7 letter word LANCING
I've seen this crossword clue in The Times
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More clues leading to the result LANCING
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The straight part
We know that "Cutting/school" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cutting/school = lancing.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 LANCING mean?
LANCING verb- To pierce with a lance, or with any similar weapon.
- To open with a lancet; to pierce
- To throw in the manner of a lance; to lanch.
- The act by which something is lanced.