David Letterman's Cue Card Guy FIRED ... For Attacking Writer

David Letterman's famous cue card guy on "Late Show" was given the boot this week ... after he says he cussed at the famous TV host backstage -- then attacked one of the writers.

Tony Mendez says he was given the boot this week over an incident that took place on Thursday ... but the real problem started the day before during a rehearsal for the show -- according to the NY Post.

Tony says he's had a problem with show writer Bill Scheft for a long time ... and during the rehearsal he snapped when Scheft interrupted his convo with Letterman -- so he told the writer to get off his back.

But when Letterman got angry at him for it Tony snapped ... telling Dave, "You're the one who has a sour disposition, mother****r."

Tony claims he was stewing all night over what happened ... and when he came into work the next day he immediately approached Scheft, then rougly grabbed him by the shirt. Sources told the Post he threw the writer up against a wall.

He was immediately removed from the building and terminated from his position -- but offered severance ... his full salary and health insurance until the show ends in May.