Griffin has taken the photo and the video explaining it offline, as has the photographer.
The president's son, Donald Trump Jr, called the imagery "disgusting but not surprising".
"I went too far", she says in her contrite follow-up video. At another point, she jokes to Shields that they're going to have to run away to Mexico after the images go public.
"CNN has terminated our agreement with Kathy Griffin to appear on our New Year's Eve program", the network's communications department tweeted Wednesday morning.
Meanwhile, Tyler told Fox News that Kathy wanted to make a political statement.
He went on to defend the photograph, saying: "That's what art is meant to do". "My children, especially my 11 year old son, Barron, are having a hard time with this". Some people look at it and they love it, some people look at it and they hate it...
Griffin then begged for the forgiveness from the audience and owned up her mistake.