In 2005, Cortez was in the ring when Tyson fought Kevin McBride. The 38-year-old Tyson was the favorite, but it soon became clear that he didn't have it in him.
Tyson faded as the rounds went on and he head-butted McBride in the sixth round -- drawing a penalty from Cortez. Tyson was pushed to the canvas at the bell and slowly returned to his corner.
Tyson's team signaled to Cortez that their fighter could not continue and Cortez stopped the fight.
Despite that history, Cortez said that he and Tyson have always shared a mutual respect.
"You have an amazing relationship with 'Iron' Mike Tyson," said Tyrus to Cortez in their Fox Nation sitdown.
"I refereed Mike Tyson on eight different occasions," said Cortez. "He told me one day, 'Mr. Cortez, I came up to you when I was 13 years old in New York. And I told you, I want to be a fighter. You gave me good advice.'"
"He said, 'Did I pass your grade?'" Cortez continued, "I said, 'Yeah, you're one of the better ones out there.'
"Mike Tyson has always respected me... since he was a young kid and he's never called me Joe, he called me Mr. Cortez."
Cortez and Tyson were inducted into the Boxing Hall of Fame in Canastota, N.Y. on the same day in 2011. It was a moment that Cortez remembered fondly.
"When I did my induction speech, the one thing that I did mention was Mike Tyson," said Cortez, known for his signature pre-fight warning to boxers, "I'm fair but I'm firm!"
"There are people out there that had a tough time making it in life," said Cortez, "Mike Tyson was one of those fighters.
"He had very difficult moments in his life growing up. He's lucky he's alive today with all the bad things that happened to him. He made it through."
Cortez was an accomplished boxer in his own right.
He was introduced to the sport when he was 12 years old and went on to win the Golden Gloves six times before turning pro when he was 18.
"It is a poor man's sport and you're looking for a way to make it in the real world," he told Tyrus. "A lot of these fighters, a lot of these champions today, they come from poverty. You know, they're really hungry. Manny Pacquiao, he was selling candy in the street.
"They can move their hands. They can punch a little bit and before you know it they're fighting for the championship," he said.
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