Rojo escaped with a yellow card from referee Craig Pawson for a two-footed lunge on Wilfried Zaha during United's 2-1 win at Crystal Palace on Wednesday.
The Argentine also avoided a red card for a similar challenge on Everton midfielder Idrissa Gueye in the 1-1 draw at Goodison Park on 4 December.
"Rojo is playing phenomenally," said Mourinho.
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Palace boss Alan Pardew described Rojo's tackle on Zaha as "dangerous".
"It's another two-footed tackle, I think he did one before [against Everton]. He was a bit fortunate to get away with that," he added.
However, Mourinho defended the former Sporting Lisbon player, adding: "He is playing really well - emotional but very clean."
Former England striker Alan Shearer, speaking on Match of the Day, said Rojo should have been sent off for his challenge on ex-United player Zaha.
"We saw it against Everton and he got away with it. You cannot tackle like that. It would have changed the game completely," added Shearer.
Wednesday's result leaves United sixth in the Premier League table, six points behind fourth-placed neighbours Manchester City and 13 behind leaders Chelsea.
United recorded back-to-back Premier League wins for the first time since August as Zlatan Ibrahimovic struck late to deprive struggling Palace of a point.
Ibrahimovic, 35, has scored nine Premier League goals since joining on a free transfer from Paris St-Germain in July.
Mourinho revealed after the Palace win that he has warned Ibrahimovic that if he wanted to end his career with a holiday, he should stay away from England.
"Zlatan has passion and plays like that. The personality is there," added the United boss.
"I told him England is not the best place to go on holiday when you are a rich guy with a phenomenal career. If you want holidays don't come to England.
"You come if you want to prove yourself, to show what you can do. His decision to come was based on that and I am very happy."
Manchester United defender Marcos Rojo is a "clean player with an aggressive nature", says manager Jose Mourinho.