At the conference Trump, when asked if he had "demonized immigrants" during the midterms campaign, replied: "No, I want them to come into the country".
A White House staff member steps in to try to take the microphone away from Acosta.
The video is below; the microphone grab is at the:18 mark.
"The White House Correspondents' Association strongly objects to the Trump Administration's decision to use US Secret Service security credentials as a tool to punish a reporter with whom it has a hard relationship", the group said.
She said his press pass was being suspended "until further notice". As a female aide attempts to take the microphone away, Acosta brushes her aside.
Journalists assigned to cover the White House apply for passes that allow them daily access to press areas in the West Wing. He regularly disrupts press conferences and uses his questions to advocate for issues he feels strongly about.
Matt Dornic, a vice-president at CNN, said: "Absolutely shameful, @PressSec".
"I worked with Jim @Acosta at CNN".
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Trump called him a "rude, bad person" before Acosta was seen refusing to give his mic to a young woman.
As anyone can see, Acosta was behaving unprofessionally for a correspondent; had he been a conservative for Fox News behaving that way in front of an Obama White House intern, the media would have castigated him as a sexist.
Acosta has been one of the most outspoken reporters covering the administration since Trump took office. Waving his finger, Trump berated him. "I never thought in this country that I wouldn't be able to go and cover the president of the United States simply because I was trying to ask a question", Acosta said. You shouldn't treat people that way.
Acosta told CNN's Anderson Cooper on Wednesday that he did not "put my hands on her or touch her as they're alleging". It was obviously a question he didn't like.
Analysis by news website Storyful said the video Ms Sanders shared "halts" and then repeats several frames in order to exaggerate Acosta's movements.
Commenting on his revoked pass on CNN, Acosta said he does think the USA government is "trying to shut us down".
"I think he embarrassed himself", he said.
Acosta said he learned that his access was withdrawn from a text message on his phone.
Mr Watson posted his defence on Twitter, saying: "Here's the video that proves I did not "doctor" or "speed up" the Acosta video, as some media outlets claim".