Mine out of spite (3)
I believe the answer is:
pit
'mine' is the definition.
(down the pit)
'out of spite' is the wordplay.
'out of' indicates a hidden word.
'PIT' is hidden within 'spite'.
(Other definitions for pit that I've seen before include "Tip into miners' shaft" , "Mine; fruit stone" , "Quarry" , "where orchestra plays" , "Hollow" .)