Wordorigins.org

Spitting image or spit and image (sometimes reanalyzed as splitting image) stems from the metaphor of spitting out an exact likeness of oneself.

The metaphor appears as early as 1602 when Nicholas Breton writes in his book Wonders Worth Hearing, “twoo girles, [...] the one as like an Owle, the other as like an Urchin, as if they had beene spitte out of the mouthes of them.”