Alternatively, sweetheart, it's a mineral (3)
I believe the answer is:
ore
'a mineral' is the definition.
(ore is a kind of mineral)
'alternatively sweetheart' is the wordplay.
'alternatively' becomes 'or'.
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'or'+'e'='ORE'
'it's' acts as a link.
(Other definitions for ore that I've seen before include "Mineral containing valuable metal" , "Rock from which metal is extracted" , "Raw material" , "not worth a lot to Danes" , "Foreign currency" .)