Jeffrey Lord tweeted “Sieg Heil” in response to an exchange with the head of Media Matters for America.
He later said his comment had been misunderstood and that he was mocking fascists.
CNN described Mr Lord as one of its best known commentators and the first explicitly pro-Trump commentator to join the network.
Mr Lord has regularly sparred with Angelo Carusone, president of Media Matters for America.
Mr Carusone, whose name had been misspelt as “Corusone” in the headline, responded: “Your headline has a mistake in it. Why do you expect anyone to take you seriously when you don’t take yourself seriously.”
Mr Lord responded with: “Sieg Heil!”
He later defended his actions, saying he was mocking Nazis and fascists, and criticised CNN’s decision to sever ties with him.
“I feel they are caving to bullies here,” he said in a telephone interview.