"They'd never recover," he said.
Trump often uses the term "hit" to mean verbally attack, rather than physical contact.
The Republican nominee zoomed in on one speaker especially, though he didn't mention his name.
"I was going to hit one guy in particular, a very little guy," Trump said to laughs at a campaign rally in Davenport, Iowa. "I was going to hit this guy so hard his head would spin, he wouldn't know what the hell happened."
Trump said this individual "came out of nowhere" and had done work with Trump in the past. "He made deals with me. 'Will you help me with this? Would you make this deal and solve the problem?' I solved the problem," Trump said.
His campaign did not respond to a request asking to clarify who Trump was talking about.
Several speakers this week have gone after Trump in Philadelphia, including Michael Bloomberg. The former New York City mayor made a surprise endorsement over the weekend for Hillary Clinton, and described Trump in his DNC speech Wednesday night as a "dangerous demagogue."
Democratic vice presidential nominee Tim Kaine also targeted Trump, mocking the businessman's tendency to accentuate his promises with a plea of "believe me."
"He said a lot of things about me, I never met the guy," Trump said. "I mean the things that were said about me. I mean, should I go through some of the names?"
Trump recalled telling a friend this week that he wanted to retaliate against the people who slammed him at the convention, mentioning current New York City Mayor Bill de Blasio by name.
"I was going to say that de Blasio is the worst mayor in the history of the city, but I didn't say it," Trump said to laughs. "He's a terrible mayor. I was going to say that, but now I won't say it."
Trump said his friend, who he labeled a "very great governor," urged him to stay focused on attacking Clinton, not other Democrats.
"He said, 'Don't hit there. Don't hit down. You have one person to beat. It's Hillary Rodham Clinton,'" Trump recalled, adding that he initially objected to the advice. "I said, 'But I really want to. I don't like what they're saying because a lot of it is lies. Not all of it but a lot of it is.' I said, 'I just really ... it makes me feel good.' "
Ultimately, he said, he conceded and decided not to launch into verbal assaults against the Democrats.
"But every once in a while I still wake up, I say 'boy, I wanna,'" Trump said, growling as he stopped himself from saying more. "Someday!"