Mitchell said in the locker room on Thursday that he's appealing the fine but had no further comment.
Mitchell was fined as a repeat offender, having already accumulated two fines for unnecessary roughness.
A source told ESPN's Jeremy Fowler that Mitchell also got an additional fine for grabbing Smith's face mask on the same play. The minimum fine for such an offense is $9,115, but Mitchell might be docked $18,231 because he's a repeat offender.
Smith has been vocal about the hit, saying he was "fired up" after the Chiefs' 19-13 loss because of the play and then calling the hit "as flagrant as it gets" on Tuesday after he had a chance to watch video of the play.
Mitchell received a 15-yard penalty for the hit. On Monday he said that he tripped and then was shoved by a teammate before hitting Smith.
"I'm not a dirty player," Mitchell said.
If anybody was likely to have an opinion about Mitchell, it would be Cincinnati Bengals wide receiver A.J. Green. Mitchell knocked Green out of a game in 2014.The jarring hit gave Green a concussion that kept him out of the 2014 AFC wild-card game. But Green just shrugged when asked about Mitchell, saying that it was part of the game.
"He tells me I'm a good player. It's all mutual respect out there," Green said. "Whatever happens out there, I don't feel he's a dirty player, man. He just plays with a lot of emotions."
"That's his style of play," Green added. "That's what makes him a starting safety in this league, and he's a good one, he's a great one."
ESPN's Katherine Terrell contributed to this report.