Diabolically his vacillating stops amiable Republican leaving (10)
I believe the answer is:
fiendishly
'diabolically' is the definition.
(I know that diabolically can be written as fiendishly)
'his vacillating stops amiable republican leaving' is the wordplay.
'vacillating' is an anagram indicator.
'stops' indicates putting letters inside (stopping can mean blocking a gap).
'amiable' becomes 'friendly' (similar in meaning).
'republican' becomes 'r' (abbreviation).
'leaving' suggests deleting specific letters.
'friendly' with 'r' taken away is 'fiendly'.
'his' anagrammed gives 'ish'.
'ish' going inside 'fiendly' is 'FIENDISHLY'.
(Another definition for fiendishly that I've seen is " Infernally clever".)