Roughly slay idol that's unfaithful (8)
I believe the answer is:
disloyal
'unfaithful' is the definition.
(synonyms)
'roughly slay idol' is the wordplay.
'roughly' is an anagram indicator.
'slay'+'idol'='slayidol'
'slayidol' anagrammed gives 'DISLOYAL'.
'that's' is the link.
(Other definitions for disloyal that I've seen before include "The opposite of 11 Across" , "Unfaithful or unpatriotic" , "Not faithful, unpatriotic" , "Violating trust" , "Faithless" .)