1520s, "to sully or stain" (the reputation, character, etc.), from Latin denigratus, past participle of denigrare "to blacken; to defame," from de- "completely" (see de-) + nigr-, stem of niger "black" (see Negro), which is of unknown origin.
The figurative sense is oldest in English; the literal sense of "blacken, make black" is recorded from 1620s. But denigrate as a past-participle adjective meaning "darkened, discolored" is attested from early 15c. "Apparently disused in 18th c. and revived in 19th c." [OED]. Related: Denigrated; denigrating.
"denigrate," by 1971, perhaps from slag (n.) in a secondary slang sense of "worthless person" (1788). Related: Slagged; slagging.
"to serve food in a dish or dishes," late 14c., from dish (n.). German tischen is "serve the table" and Swedish diska is "to wash dishes."
The modern slang meaning "to disparage, denigrate" is attested by 1940s; probably from the same figurative notion in dish it out "administer punishment" (1934). But dished meant "wasted, spent" in early 15c., presumably "used up as if made a meal of," and the same image was reborn centuries later in slang dish "frustrate, ruin, cheat" (1798), used by Byron, Scott, etc. Related: Dished; dishing.