A divine cut in America is antelope (5)
I believe the answer is:
addax
'antelope' is the definition.
(addax is a kind of antelope)
'a divine cut in america' is the wordplay.
'divine' becomes 'dd' (divine can mean theologian eg Doctor of Divinity).
'cut in america' becomes 'ax' (US spelling of 'axe').
'a'+'dd'+'ax'='ADDAX'
'is' is the link.
(Other definitions for addax that I've seen before include "Large N. Afr. antelope" , "Desert antelope" , "beast" .)