drag through the mud vs asperse

drag through the mud and asperse both are verbs.

Word	Noun	Adjective	Verb	Adverb
drag through the mud	No	No	Yes	No
asperse	No	No	Yes	No

As verbs, asperse is a hypernym of drag through the mud; that is, asperse is a word with a broader meaning than drag through the mud:

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

Other hypernyms of drag through the mud include besmirch, calumniate, defame, denigrate, slander, smear, smirch, sully.

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