Mitchell was tossed after throwing the ball at Brooks after the players tangled under the basket, while Brooks was called for a flagrant 2 foul and was also ejected following the fracas with 5:48 left and the Cavs leading 81-76.
After missing a shot and falling in the foul lane, Brooks flung his arm back and struck Mitchell, who was standing over him, in the groin area. Mitchell dropped in pain and retaliated by firing the ball at Brooks and then charging and shoving him along the baseline in front of the Memphis bench.
As the altercation threatened to spill into the seats, officials and players were able to get things under control before any punches were thrown.
Mitchell took his most vicious shots at Brooks after the game, accusing Brooks of being a dirty player and saying the NBA needs to do something about the Memphis guard's unruly bad behavior.
"That's just who he is,'' Mitchell said. "We've seen it a bunch in this league with him. Him and I have had our personal battles for years.
"There's no place for that in the game. This has been brewing for years with me and other guys in the league. You all see it. This isn't new."
It's possible the league could punish Brooks further, and Mitchell believes additional penalties are warranted.
"There should be something," he said. "This isn't just a Donovan thing. This has happened to other players throughout this league, and it's bulls--- if I'm being honest with you. It's complete bulls---. It's one thing, you know, you got Ja, you got Bane, you got Jaren Jackson. Those guys, they talk s--- and that's fine, that's all a part of basketball. We all grew up playing that way.
"But when you start doing little cheap s---, that ain't it. That's where my frustration lies. It's not about talking back and forth. That's cool, but when you start doing little stuff like that, what are we really doing?"
Cleveland coach J.B. Bickerstaff felt Mitchell, who said he has had previous run-ins with Brooks, had every right to defend himself.
"That was a cheap shot in multiple ways," he said. "A guy should have the right to stand up for himself. I thought Donovan did that. I'm proud of our guys. We don't have those guys that start s---, but we have guys who don't run from s--- and you have to in this league.
"You have to stand up for yourself. That's what he did and his teammates had his back."
Brooks refused to discuss the altercation with Mitchell in any detail. When he was asked about the exchange, Memphis All-Star Ja Morant stepped in and said the Grizzlies would not talk about the incident.
Brooks did say he agreed with the flagrant 2 call.
"It saved me some T's," he said, referring to technical fouls.
The Grizzlies have a reputation as the NBA's most talkative team, but Morant believes they're being unfairly judged.
"Anything when it comes to negative about the Grizzlies, we normally, you know, get the punishment," Morant said. "It ain't the same. They [the NBA] hate us."
While Mitchell said he and Brooks have a long history, Morant denied the Grizzlies having any issues with the four-time All-Star.
"We don't got no history with nobody," Morant said. "We don't beef with nobody."
Mitchell, who was having a tough night with just six points on 2-of-11 shooting, received a loud ovation from the sellout Cleveland crowd as he made his way to the locker room following his dismissal.
The Mitchell-Brooks tussle seemed to motivate the young Cavs. They built a 12-point lead after three quarters and pushed it to 21 in the fourth on their way to a 128-113 win to hand Memphis its seventh loss in eight games.
The Associated Press contributed to this report.