The host was speaking with Sarah Burge, a British woman who describes herself as the "human Barbie" and spent £250,000 ($392,000) on cosmetic procedures.
However, when Burge spoke about allowing her 15-year-old daughter to have Botox to stop her from sweating, Cooper began to take offence.
He revealed that a cosmetic surgery expert had told him there is "no medical indication" for a teenager to need the procedure, but Burge replied: "Well, in that case he doesn't know what he's talking about because there is medical indications."
Burge added that her daughter wants Botox to stop her from sweating during performances, adding: "You wouldn't see Beyoncé sweating on the stage."
Cooper disagreed, while Burge continued: "I would prefer to actually oversee my daughter's Botox than actually have her go underground finding a voodoo witch doctor or in fact getting it off the internet and administering it herself."
Cooper paused, before admitting that he had "nothing more" to speak with Burge about as the audience clapped.
"I've got to be honest," he said. "I've got to just stop... I try to be really polite to all my guests, I just think you're dreadful and I honestly don't want to talk to you anymore, so I'm just going to stop."
Burge repeated "That's fine" as she walked off the stage.
According to E! News, Cooper later added backstage: "I got the feeling this was about publicity for her. I regret having her on in the first place and I regret how things ended."
Burge has previously caused controversy by buying her 8-year-old daughter cosmetic surgery vouchers for her birthday.