Crossword Genius

Cross punched into a heel designed to let air out (6)

Ross

I believe the answer is:

exhale

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'cross punched' is the definition.
I can't judge whether this definition defines the answer.

'into a heel designed to let air out' is the wordplay.
'into' is an insertion indicator.
'designed' indicates an anagram (designed with the letters).
'to let air out' becomes 'x' (I can't justify this - if you can you should give a lot more credence to this answer).
'a'+'heel'='aheel'
'aheel' anagrammed gives 'ehale'.
'ehale' placed around 'x' is 'EXHALE'.

Can you help me to learn more?

(Other definitions for exhale that I've seen before include "Expel air from the lungs" , "produce emissions" , "Joint of chicken" , "expire" , "Puff away" .)

I've seen this clue in The Independent.
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