Son was sent off in the second half after VAR ruled he kicked out at Cheleea defender Antonio Rüdiger.
At first, referee Anthony Taylor overlooked the incident but VAR checked it and deemed he was guilty of violent conduct, ending up with a red card.
Tottenham are now waiting for news from the Football Association to see whether he will be available for Boxing Day’s clash with Brighton.
“I hope Son is not punished five times,” Mourinho said, according to the Guardian UK.
“One time was the foul that Rüdiger did on him. The second is to be sent off. The third would be not to play against Brighton.
“The fourth not to play against Norwich and the fifth not to play against Southampton. So I hope to be punished twice is enough, he doesn’t deserve for the third the fourth or the fifth.
“Mr Paul Tierney decides yes and Mr Anthony Taylor who was in the game, in real time, five metres from the situation, Mr Taylor decided no.
“So who was refereeing the game? Not Mr Taylor. It was Mr Tierney. I think not a red card, VAR was to support football, to bring true football, to bring true to the spectacle and they did that with the penalty decision and they killed the game with Son’s decision. The situation with Son, I think Mr Tierney made it wrong. It’s the wrong call.
“This is England, this is the Premier League, this is the best competition in the world, with characteristics that if we change them we are killing the best league in the world. Mr Taylor had the feeling, he was there, he saw it clearly so I think it’s the wrong call.”
If Spurs are not successful in their appeal, the South Korean, will miss the game. If that is the case, Mourinho says his side will have to fight an “injustice.
“It would be a big loss,” the Portuguese said.
“We don’t have a big squad. We don’t have lots of players.
“This moment is a moment where it is normal to think about rotations and very difficult situations for players to play every game.
“We don’t have [Érik] Lamela and it’s a big loss for us. But if that happens then we have to try to cope with it and to fight against injustice. But the way to fight against injustice is to give our best and the boys that are going to play are going to try and get results in it.”