Minister's job can be dispiriting (8)
I believe the answer is:
exorcism
I believe this is a double definition.
'minister's job' is the first definition.
(a church minister might perform an exorcism)
'be dispiriting' is the second definition.
(removing evil spirits)
'can' is the link.
(Other definitions for exorcism that I've seen before include "Religious ceremony for driving out an evil spirit" , "Ritual of expelling evil spirits" , "Dispossession" , "Ritual of driving out demons" , "Ceremony of driving out evil spirit by prayer" .)