Acosta attempted to ask another question about the Mueller probe, but Trump dismissed him by repeatedly saying, "That's enough", and motioning for Acosta's microphone to be handed to another reporter.
"We stand by our decision to revoke this individual's hard pass".
In a later tweet, Mr Acosta said Ms Sanders' assertion he placed his hands on the woman was "a lie".
In a news conference on Wednesday, Acosta was trying to challenge Trump over the president's scare-mongering about the so-called "caravan" of migrants making their way through Mexico.
After asking his follow-up question, the staff member takes the microphone off Acosta and hands it to the next journalist.
"[Trump] came out right after his inauguration and said his inauguration crowds were bigger than President Obama's, when they weren't", Acosta previously said in a CNN segment.
"CNN should be ashamed of itself having you work for them", the president said to Mr Acosta.
"They are not only unsafe, they are disturbingly un-American", the network said.
President Donald Trump struck back at a black female reporter's question about his calling himself "nationalist" as "emboldening white nationalists", calling it a "racist question", "insulting", and "very bad".
His organization "absolutely" would support such an effort, he said, and suggested a larger framing might be wise - one that includes the Trump Justice Department's efforts, now before the D.C. Circuit Court of Appeals, to undo the $85 billion merger between AT&T and Time Warner, which is CNN's parent company.
"Do you think they were actors?"
Trump clearly does not agree. To Jim Acosta, as he tried to explain the migrant caravan to the president: 'Thank you for telling me that, I appreciate it.'11.
It also feeds the kind of anti-media controversy Trump loves to generate, and which benefits him politically.
Stirewalt said that either way, the episode hurts the political discourse as the Acosta-Trump feud overshadowed "a bunch of good questions" from reporters like Fox News' John Roberts and CBS News' Major Garrett.
She did not say to whom she was referring, but the implication was that it was Acosta.
Acosta was asked by an agent of the US Secret Service for his accreditation after leaving the presidential building, according to a video of the moment shared by the journalist on Twitter.
"While President Trump has made it clear he does not respect a free press, he has a sworn obligation to protect it", CNN said in a statement.
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".
The WHCA called on the White House to "immediately reverse this weak and misguided action".