Brace yourselves for this, straight from Oxford.

"Spitting image" is a now standard phrase that was originally a hypercorrection of...

"Spittin' image," which was a hypercorrection of...

"Spitten image," which the OED regards as "nonstandard," and which was a misconstrual of...

"Spit and image," which the editors consider perfectly standard, and which was a variation of the seminal and equally standard "very spit of."

Why exactly "spit" should have been used this way is uncertain, though uncouth possibilities do come to mind.