Part of ugly sister destroying process (5)
I believe the answer is:
lysis
'process' is the definition.
(lysis is a kind of process)
'part of ugly sister destroying' is the wordplay.
'part of' indicates a hidden word.
'LYSIS' can be found hidden inside 'ugly sister destroying'.
(Other definitions for lysis that I've seen before include "Decline" , "Disintegration of a cell by rupturing" , "Breaking down" .)