Spitting image and related phrases (e.g. "he's the [very] spit[ting] [image/picture]") are 19th century. It appears it did come from the word spit rather than split.
Its roots may be found in the 17th century, in
He resembled him in euerie part; he was as like him as if he had beene spit out of his mouth.
This is found in a 1611 French-English dictionary with a similar French translation. Perhaps the English phrase was translated from the French, or perhaps the other way round, or perhaps both phrases were current in each language.
The OED says spitting image (1901) it's an alteration of spitten (image, picture) (1878). This in turn is a corruption of spit and (image, picture, fetch) (1859). The very spit of is 1825.
Curiously, splitting image (or splitten image) is recorded later (1880).
I found an antedating for spitting image from Hall Caine's A Son of Hagar, volume 2 (first published 1886, this edition 1887):
' Blest if you don't look the spitting image
of a friend of mine — 'boutn the eyes, I mean
— red and swelled up and such.
The Dialect of Cumberland (1873) by Robert Ferguson suggests it is really from spit:
SPITTEN-PICKTER. sb. " Strong likeness. Yon barn's his varra spitten-picter." — Dick. "That barn's as like his fadder as an he'd been spit out of his mouth." — Crav. The expression was used in Early Eng. "He was as like him as if he had been spit out of his mouth." — Cotg.
Those references are:
- Dick.: A Glossary of Words and Phrases Pertaining to the Dialect of Cumberland (1859) by William Dickinson
- Crav.: The Dialect of Craven (1828) "By A Native of Craven"
- Cotg.: A Dictionary of the French and English Tongues (1623) by Randle Cotgrave
Here's the second, The Dialect of Craven: In the West-Riding of the County of York (1828):
SPIT, That barn's as like his fadder, as an he'd been
spit out of his mouth," i. e. he very much resembles
him. " C' estoit luy tout craché ;" he resembled him
in every part, he was as like him, as if he had been
spit out of his mouth. Cotgrave. Non tarn ovum
The Latin "Non tarn ovum ovo simile" can be more directly translated as "as like as one egg to another".
Here's Randle Cotgrave's A Dictionary of the French and English Tongues (this one 1611):
Craché: m.ée: f. Spet, or spatled out; spattered, bespawled.
C' estoit luy tout craché ; He resembled him
in euerie part; he was as like him as if he had beene
spit out of his mouth.