1560s, "to thrust out, remove, throw out of doors," from Latin eliminatus, past participle of eliminare "thrust out of doors, expel," from ex limine "off the threshold," from ex "off, out" (see ex-) + limine, ablative of limen "threshold" (see limit (n.)).
Used literally at first; the sense of "exclude, throw aside, or disregard as undesirable or unnecessary" is attested by 1714; the sense of "expel waste from the body" is by c. 1795. Related: Eliminated; eliminating; eliminative; eliminatory.