slur (n.)
"deliberate slight, disparaging or slighting remark," c.1600, from dialectal slur "thin or fluid mud," from Middle English slore (mid-15c.), cognate with Middle Low German sluren, Middle Dutch sloren "to trail in mud." Related to East Frisian sluren "to go about carelessly," Norwegian slora "to be careless." Literal sense of "a mark, stain, smear" is from 1660s in English. The musical sense (1746) is from the notion of "sliding." Meaning "act or habit of slurring" in speech is from 1882.
slur (v.)
c.1600, "smear, soil by smearing," from slur (n.). Meaning "disparage depreciate" is from 1650s. In music, from 1746; of speech, from 1893. Related: Slurred; slurring.