malign vs asperse

malign is an adjective but asperse is not an adjective.

Word	Noun	Adjective	Verb	Adverb
malign	No	Yes	Yes	No
asperse	No	No	Yes	No

As verbs, asperse is a hypernym of malign; that is, asperse is a word with a broader meaning than malign:

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

Other hypernyms of malign include besmirch, calumniate, defame, denigrate, slander, smear, smirch, sully.

malign (adjective)	asperse (adjective)
evil or harmful in nature or influence
having or exerting a malignant influence

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