The most common and most likely answer to this crossword clue is the 9 letter word CALUMNIED
I've seen this crossword clue in The Times
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The straight part
We know that "Bad-mouthed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bad-mouthed = calumnied.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CALUMNIED mean?
CALUMNIED verb- To make false accusations or levy false charges against a person with the intent to tarnish that person's reputation or standing; to calumniate.