Mexico’s right, somehow, dispatching spirits (8)
I believe the answer is:
exorcism
'dispatching spirits' is the definition.
(removing evil spirits from a place or person)
'mexico's right somehow' is the wordplay.
'right' becomes 'r' (common abbreviation).
'somehow' indicates anagramming the letters.
'mexicos'+'r'='mexicosr'
'mexicosr' anagrammed gives 'EXORCISM'.
(Other definitions for exorcism that I've seen before include "Dispossession" , "Ritual of driving out evil spirit" , "Ritual to banish evil spirits" , "Ceremony to release evil spirits" , "Religious ceremony for driving out an evil spirit" .)