EXCLUSIVE

Discovery Channel's breakout hit "Fast N' Loud" just booted two of the show's most popular characters ... and one of the jobless guys says it's because they were fast with swearing at a manager ... and loud.

Tom Smith tells TMZ ... he and co-star Jordan Butler were sacked from the Gas Monkey Garage -- the auto shop featured in the show -- after they let a fan with cystic fibrosis pose for a pic next to a Rolls-Royce owned by shop owner Richard Rawlings﻿.

Smith claims the manager on duty flipped out and told them to "get the f*** away from the car." Now here's the big mistake ... we're told Smith yelled back, "Chill the f*** out" -- something boss men don't take kindly to. So Rawlings fired them both a few hours later.

Rawlings tells TMZ he's had nothing but problems with the 2 guys.