Cut fuel used by American hospital (4)

I believe the answer is:

gash

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'cut' is the definition.
(a gash is a wound or cut)

'fuel used by american hospital' is the wordplay.
'fuel' becomes 'gas' (gas is a fuel).
'used by' says to put letters next to each other.
'american hospital' becomes 'h' (abbreviation for hospital on maps. I am not sure about the 'american' bit.).
'gas'+'h'='GASH'

Can you help me to learn more?

(Other definitions for gash that I've seen before include "Gaping wound" , "Long deep wound" , "Cut; waste (colloq.)" , "surplus to requirements" , "injury" .)

I've seen this clue in The Independent.

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