Where does the phrase "dead simple" originate?

Dead here means utterly, absolutely, which is not a slang usage. Etymonline suggests that it hails from the 14th century, but does not explain whence it derived:

Used from 16c. in adj. sense of "utter, absolute, quite" (cf. dead drunk first attested 1590s; dead heat, 1796). As an adv., from late 14c. Dead on is 1889, from marksmanship.

I would guess the following: death -> permanence -> absoluteness. But this is all speculation. I doubt you'll ever find an authoritative history of this evolution.

In expressions like dead simple, dead easy, dead on, or dead right, dead is used as an adverb, meaning completely or extremely.

Etymonline indicates some of the history:

Used from 16c. in adj. sense of "utter, absolute, quite" (cf. dead drunk first attested 1590s; dead heat, 1796). As an adv., from late 14c. Dead on is 1889, from marksmanship.