drag through the mud vs defame

drag through the mud and defame both are verbs.

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

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

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

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

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