The term 'drag through the mud' is an idiom that means to damage someone's reputation by spreading false or negative information. The crossword solutions for this term are TRADUCE (7 letters), SLUR (4 letters), bemire (6 letters), DISCREDIT (9 letters), MALIGN (6 letters), DEFAME (6 letters), SMEAR (5 letters), and LIBEL (5 letters). All of these words have similar meanings, which involve damaging someone's reputation by making false or negative statements about them.