Mitchell posted a statement on social media, in which she described the stand-up artist as a "decent person".
The presenter was inundated with a torrent of negative comments, with netizens accusing her of being indifferent to the suffering of the victims of crimes committed by the Nazis.
Other users accused her of supporting a "racist" comedian.
The Joke and The Reaction
"I think we all have come to terms with the fact, I get cancelled in the next couple of years, right? Yeah, chances are. Here is the good news. I'm going down swinging", the comedian said.
He then went on to joke about various subjects mentioned above before reaching the ultimate career ender – the Holocaust.
"When people talk about [it], they talk about the tragedy and horror of six million Jewish lives being lost to the Nazi war machine. But they never mention the thousands of Gypsies that were killed by the Nazis. No one ever wants to talk about that because no one ever wants to talk about the positives", he said.
WARNING: This video contains strong language.
Jewish organisations and anti-hate groups described the joke as "abhorrent". The Holocaust Memorial Day Trust said it was "absolutely appalled" by it.
"Hundreds of thousands of Roma and Sinti people suffered prejudice, slave labour, sterilisation, and mass murder simply because of their identity - these are not experiences for mockery", the organisation said.
The Traveller Movement, a charity which supports the Roma community, said the joke was "truly disturbing and goes way beyond humour", while an anti-racism group called Hope Not Hate accused Carr of "celebrating" the suffering of the Roma and Sinti people.
Neither Netflix nor the comedian has commented on the issue. Carr previously touched on the issue of edgy jokes, including in the latest special. The stand-up artist said he comes up with dark humour only to make people laugh and not offend anyone.
"You've enjoyed the evening, right", the comedian asked the audience. "I hope none of you needed it. Sometimes you need it. When life is s**t, that is when you need a laugh. It's best to have a very dark sense of humour, right? Because at least when our life is s**t, we can laugh about it. I feel sorry for the people that get offended for those that can't laugh at dark s**t. Because when their life is terrible they have just got to f**king white-knuckle it", he said.
"I felt like I would be shortchanging them if didn't [mention those issues]. So I walked up on stage, with some degree of trepidation in front of 200 people dying of cancer. I said 'Come on, we haven't got have much time. Well, I have'. And the laugh was extraordinary. It was like the volume had been turned up and suddenly there was air in the room, and this dark ominous presence was taken down and laughed at", Carr said.