drag through the mud vs smear

drag through the mud is not a noun while smear is a noun.

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

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

drag through the mud: speak unfavorably about
smear: 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, defame, denigrate, slander, smirch, sully.

drag through the mud (noun)	smear (noun)
	an act that brings discredit to the person who does it
	a blemish made by dirt
	a thin tissue or blood sample spread on a glass slide and stained for cytologic examination and diagnosis under a microscope
	slanderous defamation

drag through the mud (verb)	smear (verb)
speak unfavorably about	charge falsely or with malicious intent; attack the good name and reputation of someone
	make a smudge on; soil by smudging
	stain by smearing or daubing with a dirty substance
	cover (a surface) by smearing (a substance) over it