Clue is roundly trashed in a cynical manner (13)

I believe the answer is:

incredulously

'in a cynical manner' is the definition.
(in a disbelieving manner)

'clue is roundly trashed' is the wordplay.
'trashed' is an anagram indicator.
'clue'+'is'+'roundly'='clueisroundly'
'clueisroundly' with letters rearranged gives 'INCREDULOUSLY'.

(Another definition for incredulously that I've seen is " viewed with scepticism".)

I've seen this clue in The Times.

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