'Kitchen Nightmares' Star -- Threatens to Kill Restaurant Patron ... WITH A KNIFE

Amy's Baking Company founder Samy Bouzaglo -- who appeared on "Kitchen Nightmares" -- attacked someone with a knife outside his restaurant Saturday ... and the footage is CRAZY!

The person who shot the video says a drunk guy was eating at the Scottsdale restaurant when Samy's wife Amy Bouzaglo became enraged and ordered him to leave -- and he did.

But Samy wasn't done with him. The video shows him outside -- waving a knife  -- going after the guy. You hear him scream to his wife, "Let me!"

Samy eventually backed off, the guy left.

We called the Bouzaglo's ... and they INSIST Samy was holding a pen -- not a knife.