Green’s Dictionary of Slang

eat me! excl.

also eat my meat!
[eat v. (4)]

(US) shut up! you make me sick! the hell with you! go away!

[US]Guild Dict. Homosexual Terms 14: eat me! (v.): An unfriendly term meaning: ‘Shut up,’ ‘Go to hell,’ etc. It is usually used by the heterosexual but does not mean to -fellate although its unfriendly meaning is drawn from the heterosexual’s low regard for the homosexual in this sex act.
[US]S. King Long Walk in Bachman Books (1995) 230: ‘Eat my meat,’ Barkovitch snarled.
[US] P. Munro Sl. U.
[US]C. Hiaasen Lucky You 29: ‘S’matter? You ain’t fond of these Negro rappers?’ ‘Eat me,’ Bode Gazzer said.
[US]W. Ellis Crooked Little Vein 137: ‘Please regulate your language in here, ma’am.’ [...] ‘Eat me.’.