The president said he had only "recently" learned of the allegations against his former aide and was surprised.
Wynn "has been accused and has been condemned without any due process", Mulvaney said.
And staff secretary Rob Porter stepped down Wednesday after abuse allegations from two ex-wives became public that he too denied.
CBS News White House correspondent Major Garrett pointedly asked Mulvaney, "Why shouldn't women reasonably wonder if this White House doesn't have a lax attitude when it comes to the question of domestic abuse?"
Trump's White House aides may leak a message that POTUS is outraged over Porter's alleged abuse, but publicly Trump doesn't seem to blame Porter at all.
"Why not use this as an opportunity to say something like that?" the reporter wondered. "Now, he also, as you probably know, he says he's innocent, and I think you have to remember that".
In December, Trump defended Senate hopeful Roy Moore, who had been accused of having inappropriate sexual relationships with teenagers when he was an adult.
Kelly has indicated he would step aside if he lost the faith of the president.
Last Friday, Kelly made it clear that he would resign if the President wanted him to, a source with knowledge of the matter told CNN. "The process for the background check was ongoing and the White House had not received any specific papers regarding the completion of the background check". Porter has denied both allegations.
A group of twelve Democratic senators sent a letter Friday to chief of staff John Kelly and White House counsel Don McGahn asking when they first knew of the domestic abuse allegations against Porter by his ex-wives.
Porter resigned or was sacked Wednesday, a day after Kelly had defended him as "a man of honor" in a statement in which Hicks apparently had a hand.More news: Barclays Trims AA (LON:AA) Target Price to GBX 200
She reiterated Sunday that she detailed her experience to the Federal Bureau of Investigation before Sorensen was hired at the White House.
Kellyanne Conway, a senior advisor to Trump, said president pushed the two staffers out the moment he saw credible evidence against them.
In a lengthy statement provided to the Post, Sorensen said he had "never committed violence of any kind against any woman in my entire life".
Willoughby said this is not related to politics, however.
She pointed out just how risky it is that our culture is so ready to question victims of abuse rather than simply believe them.
Sanders faced a flurry of questions about the White House's handling of Porter, who resigned last week after his ex-wives' accounts were published by the DailyMail.com and The Intercept.
But the president's latest comments suggest that this week's resignations - particularly Porter's - were jolting at the highest levels. In fact, I wrote a book and came out and was very tough on President Clinton at the time. "And certainly he's also very sad".
Other White House aides went on Sunday television news shows to stress that Mr Kelly's job was safe.
"That's like saying that axe murderer out there, he's a great painter", said former Vice President Joe Biden. "Because, consistently, their actions tell us they don't".
"You want to stop a four-star general who is running the White House, who believes in chain of command, who makes a decision within 40 minutes, because you hate President Trump?".