Green’s Dictionary of Slang

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

1965		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.
1979		S. King Long Walk in Bachman Books (1995) 230: ‘Eat my meat,’ Barkovitch snarled.
1989		P. Munro Sl. U.
1997		C. Hiaasen Lucky You 29: ‘S’matter? You ain’t fond of these Negro rappers?’ ‘Eat me,’ Bode Gazzer said.
2007		W. Ellis Crooked Little Vein 137: ‘Please regulate your language in here, ma’am.’ [...] ‘Eat me.’.
2023		(con. 1962) J. Ellroy Enchanters 141: I flashed my credential, Motel Mike lip-synched Eat me.