Crossword Genius

Not happy about, we gave the chop to (5)

Ross

I believe the answer is:

sawed

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'the chop to' is the definition.
I can't tell whether this defines the answer.

'not happy about we' is the wordplay.
'not happy' becomes 'sad' ('sad' is the opposite to 'happy').
'about' means one lot of letters goes inside another.
'sad' enclosing 'we' is 'SAWED'.

'gave' acts as a link.

Can you help me to learn more?

(Other definitions for sawed that I've seen before include "Cut through wood" , "Cut with a toothed blade" , "Cut with edged tool" .)

I've seen this clue in the Evening Standard.
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