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."

Motorcyclist Leighton Santos, 22, admitted causing David Hitchen's death through careless driving and was jailed at Preston Crown Court on Monday.
The maximum sentence is five years, but this can be reduced by a guilty plea.
Road safety charity Brake said there was a "need to see much tougher sentences when a driver has killed".
Santos admitted causing the 42-year-old former Great Britain international's death near Belmont, Lancashire, in September 2014, on the first day of his trial.
Lancashire Police said Santos had been riding a Yamaha motorbike on Rivington Road when he "drifted into the opposite carriageway" and collided with Mr Hitchen.
The cyclist suffered serious injuries and died later in hospital.
In addition to the six months for causing death by careless driving, Santos was also given 12 months for another motoring offence.
In March 2016 he was convicted at Manchester Crown Court of dangerous driving after taking police on an eight-mile pursuit that saw him reach speeds of up to 90mph (145km/h) in a 30mph zone.
Martin Key, British Cycling's campaigns manager, said six months for "causing the death of a human being is a punishment that many would agree certainly does not fit the crime".
"While these incidents are extremely rare, we need to ensure that sentencing guidelines adequately reflect the potential consequences of an offence," he said.
A spokeswoman for Brake said the sentence was "insulting".
"Leighton Santos, who killed another human being, was sentenced to a paltry 18 months in prison, and will likely be out in nine.
"It's no wonder that grieving relatives are often left feeling let down and insulted by our justice system.
"We need to see much tougher sentences when a driver has killed, particularly when, as in this case, they have exhibited previous examples of dangerous behaviour."
Manchester United defender Marcos Rojo is a "clean player with an aggressive nature", says manager Jose Mourinho.
[NEXT_CONCEPT]
A six-month prison term handed to a motorist who killed an ex-international cyclist in a crash "does not fit the crime," British Cycling has said.