Reason American soldier cuts hair short (5)
I believe the answer is:
logic
'reason' is the definition.
(logic is using reason)
'american soldier cuts hair short' is the wordplay.
'american soldier' becomes 'GI' (informal term for a US soldier).
'cuts' means one lot of letters goes inside another (some letters cut their way into other letters).
'hair' becomes 'lock' (a lock of hair).
'short' means to remove the last letter.
'lock' with its last letter taken off is 'loc'.
'gi' placed inside 'loc' is 'LOGIC'.
(Other definitions for logic that I've seen before include "The science of reasoning correctly" , "Rational thinking" , "Strict reasoning" , "Rigorous reasoning" , "Sound reasoning" .)