The most common and most likely answer to this crossword clue is the 10 letter word SHORTENING
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result SHORTENING
Buddy explains!

The straight part
We know that "Cutting down/fat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cutting down/fat = shortening.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 SHORTENING mean?
SHORTENING verb- To make shorter; to abbreviate.
- To become shorter.
- To make deficient (as to); to deprive (of).
- To make short or friable, as pastry, with butter, lard, etc.
- To reduce or diminish in amount, quantity, or extent; to lessen.
- To take in the slack of (a rope).
- To reduce (sail) by taking it in.
- Fat that is solid at room temperature, such as margarine or lard (not usually used of butter), used to make shortcrust pastry.
- Verbal noun of shorten - a reduction in length.