In the clip, Acosta asks the president about his use of the word "invasion" to describe the caravan of between 3,600 to 7,200 Central Americans that is advancing toward the US-Mexico border. The migrants hope to receive asylum in the US. Acosta also asks Trump whether he has demonized immigrants
"Here we go," Trump interrupts Acosta as the journalist begins to ask his question, following with a statement that he wants immigrants to "come in legally."
"I think you should let me run the country, you run CNN, and if you did it well, your ratings would be much better," Trump tells Acosta.
When the president tries to call on another journalist, Acosta refuses to give up the microphone and asks about special counsel Robert Mueller probe into Russia's alleged meddling in the 2016 presidential election.
"That's enough. That's enough. That's enough. That's enough," Trump says, ordering him to "put down the mic," as a White House staffer tries to grab the microphone from the CNN correspondent.
When Acosta finally gives up the mic and sits down, Trump begins to chide him.
"CNN should be ashamed of itself, having you working for them," Trump says. "You are a rude, terrible person. You shouldn't be working for CNN…. You're a very rude person. The way you treat [White House Press Secretary] Sarah Huckabee [Sanders] is horrible. And the way you treat other people is horrible. You shouldn't treat people that way."
The president then moves to answer the next question by NBC News White House correspondent Peter Alexander, who takes the opportunity to defend Acosta.
"In Jim's defense, I've traveled with him and watched him. He's a diligent reporter who busts his butt like the rest of us," Alexander said.
"Well, I'm not a big fan of yours either," Trump retorts. Acosta then stands up once again and begins asking questions, but Trump cuts him off: "When you report fake news, which CNN does a lot, you are the enemy of the people."
This is not the first time Acosta has asked controversial questions on air. During a White House press briefing last month, Acosta tried to force Sanders to spell out which news outlets are considered to be the "enemy of the people."
"If the president is going to say that the fake news media are the enemy of the people, and you're going to stand there and continue to say that there are some journalists with some news outlets in this country with that characterization, shouldn't you have the guts, Sarah, to state which outlets, which journalists, are the enemy of the people?" he asked.
Later during the conference Wednesday, Trump snapped at Yamiche Alcindor, White House correspondent for PBS, who asked him whether his embrace of "nationalism" emboldens white nationalists.
"I don't know why you'd say that," Trump said. "That's such a racist question."
Trump has repeatedly denounced the mainstream media, calling it the enemy of the people.
Following the testy confrontations, CNN tweeted that Trump's "ongoing attacks on the press have gone too far."
"They are not only dangerous, they are disturbingly un-American. While President Trump has made it clear he does not respect a free press, he has a sworn obligation to protect it. A free press is vital to democracy, and we stand behind Jim Acosta and his fellow journalists everywhere," the statement read.
UPDATE: The White House has suspended Acosta's hard pass to visit the White House as a reporter.
"The fact that CNN is proud of the way their employee behaved is not only disgusting, it is an example of their outrageous disregard for everyone, including young women, who work in this Administration. As a result of today's incident, the White House is suspending the hard pass of the reporter involved until further notice," White House spokeswoman Sarah Sanders said in a statement Wednesday evening to Reuters.