badmouth vs slander

badmouth is not a noun while slander is a noun.

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

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

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

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

badmouth (noun)	slander (noun)
	an abusive attack on a person's character or good name
	words falsely spoken that damage the reputation of another

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