The actor was working at Scotland's Dundee Rep Theatre when the accident took place, while he was being taught how to handle prop weapons. He accidentally pulled the trigger, but fortunately the pistol fired blank cartridges.
"I was the worst stage manager, I was hopeless, and there was one horrific incident," Cox tells the "Great Scot!" podcast. "The worst incident was I burned this guy's nose. He was teaching me how to hand a gun to somebody, because in those days we used to have pistols that fired blanks. He said, 'You never hand the gun to somebody with the barrel pointing at them and you hand it with the chamber open.' "
"So I'm taking the gun as he's handing it to me and then I hit the trigger and it went bang. It went black and he had a burned nose. I still had a job after it. They blamed it on themselves for not instructing me properly."
Cox currently stars as media magnate Logan Roy on HBO's "Succession". The acting vet said playing the media mogul has been the highlight of his 60-year career, having earned a Golden Globe Award for best actor and being nominated for an Emmy Award for his role on the series.