1775, American English dialectal, "troublesome person or animal" (usually with a defining adjective), a vulgar pronunciation of curse (n.), or else a shortening of the slang sense of customer. The word in the literal sense of "a curse" is from 1848.
1815, "to say bad words, use profane language," a vulgar pronunciation of curse (v.). Transitive sense of "to curse, swear at" is by 1838. Related: Cussed; cussing. To cuss (someone) out is attested by 1881.