What is the meaning and etymology of 'scut' from 'scut work'?

In the Wiktionary scutwork entry, one of the references, Medical meanings: a glossary of word origins, suggests either scuttle, or OE scitan (excrement) as possible origins of the scut in scutwork. I think scitan is plausible; note from the etymology of shit:

Noun use for "obnoxious person" is since at least 1508

Wiktionary also suggests for scut as "contemptible person" that the etymology may be from the obsolete sense of scout, which Etymonline explains:

"to reject with scorn," c.1600, of Scandinavian origin (cf. O.N. skuta, skute "taunt"), probably from a source related to shout.

I think you're probably right that meaning (2) of scut is more closely related to scutwork, but note that calling someone contemptible doesn't have to be unrelated to meaning (1) as in the quotations in Wiktionary, or, for example, this 1907 story:

"Don't understand me?" roared the farmer. "What have you done to my darter, you scut, sitting there preening of yersel, like a silly peacock in the sun?"
The angry man approached the bed swiftly, and, seizing Aubrey's pyjama-clad shoulder in a massive fist, thrust his hairy face within an inch of his victim's nose.
"What have you been doin' to my lass?" he roared again. "Now d'yew onderstand me?"
"W-what has she been telling you?" Aubrey was horribly frightened.
"Summat that made me sware you shouldn't leave this house till you'm man and wife all raight and praper accordin' to law."

This is not a definitive answer, because all the sources I checked say the origin is not known. But I suspect it probably comes from scuttle, because doing the dishes is the archetypal form of "scut" work, and as Etymonline shows us:

scuttle (n.) "bucket," O.E. scutel "dish, platter," from L. scutella "serving platter," dim. of scutra "flat tray, dish," perhaps related to scutum "shield" (see hide (n.1)). A common Gmc. borrowing from Latin (cf. O.N. skutill, M.Du. schotel, O.H.G. scuzzila, Ger. Schüssel). Meaning "basket for sifting grain" is attested from mid-14c.; sense of "bucket for holding coal" first recorded 1849.

"Scut work" was in use at least as early as 1950. From The Yale Journal of Biology and Medicine, Volume 22:

... menial tasks commonly known as the "scut work."

Given the general manners of the time, it seems unlikely that this would be used too pejoratively.

James Joyce's, Finnegans Wake (1939) also refers to a character as a "scutfrank" -- which has been interpreted to mean someone who does menial tasks.