badmouth vs calumniate

badmouth and calumniate both are verbs.

Word	Noun	Adjective	Verb	Adverb
badmouth	No	No	Yes	No
calumniate	No	No	Yes	No

As verbs, calumniate is a hypernym of badmouth; that is, calumniate is a word with a broader meaning than badmouth:

badmouth: speak unfavorably about
calumniate: charge falsely or with malicious intent; attack the good name and reputation of someone

Other hypernyms of badmouth include asperse, besmirch, defame, denigrate, slander, smear, smirch, sully.

badmouth (verb)	calumniate (verb)
speak unfavorably about	charge falsely or with malicious intent; attack the good name and reputation of someone