Reason to record diamonds being cut (5)
I believe the answer is:
logic
'reason' is the definition.
(logic is using reason)
'record diamonds being cut' is the wordplay.
'record' becomes 'log' (logging is a kind of recording).
'diamonds' becomes 'ice' (slang term for diamonds).
'being cut' means to remove the last letter.
'ice' with its last letter taken away is 'ic'.
'log'+'ic'='LOGIC'
'to' acts as a link.
(Other definitions for logic that I've seen before include "Reasoned thinking" , "Branch of philosophy that analyses inference" , "Chain of reasoning" , "Rational thinking" , "using premises" .)