Trump and Acosta have long have a contentious relationship as the CNN reporter often asks the president questions that seemed created to illicit a reaction from him.
The video appears to be taken from fringe far-right website InfoWars to make it look like Acosta chopped down on the intern's arm.
Sanders' tweet of the edited video, in which she said the White House would "not tolerate the inappropriate behaviour clearly documented in this video", has at least 20,000 retweets and more than 2 million views.
Eventually NBC reporter Peter Alexander took the microphone and defended his fellow reporter, despite him being from a separate network, calling him a "diligent reporter" - which only proved to anger Trump more.
"It was done in retaliation for his challenging questions at today's press conference", CNN communications said in a statement posted to Twitter. Acosta started his question by quoting a poem etched at the base of the Statue of Liberty and asked whether the government was rigging the system for Great Britain and Australia.
"When you report fake news, which CNN does a lot, you are the enemy of the people", Trump said to Acosta when he protested again.
Acosta responded that Sanders' description of events was "a lie".
A White House staff member reaches for the microphone held by CNN's Jim Acosta during a news conference at the White House in Washington, November 7, 2018.
Mr Trump took the rare step of mocking Republican candidates who kept their distance from him during the campaign because of concerns that his divisive messages on immigration would turn off voters - but lost anyway.
Democrats win House control
In south Florida , former Health and Human Services Secretary Donna Shalala defeated Republican Maria Elvira Salazar. The Democrats benefited from extraordinary voter enthusiasm, robust fundraising and unusually fresh candidates.
Trump frames midterms as ‘tremendous success’
The GOP's successes were fueled by a coalition that's decidedly older, whiter, more male and less likely to have college degrees. More women than ever were running, along with veterans and minorities, many of them motivated by revulsion over Trump.
3 found dead in collapsed buildings
The neighbourhood is home to many buildings in a similarly dilapidated condition, some of them run by slum landlords. An adjoining third building, number 67, sustained damage and was torn down for fear it would collapse, as well.