American challenger 'Big Baby' Miller gave unified champion Joshua an almighty shove as they came together before a word was even spoken at New York's Madison Square Garden, where their title fight will be held on June 1.
It will be Joshua's first fight outside the UK, where he is a major star. The Englishman and his team are now keen to establish their brand across the pond.
Joshua, the IBF, WBA, WBO and IBO world champion, also clashed with Miller last year, when the brash New Yorker crashed the stage during a press event ahead of the Englishman's fight with Russian Alexander Povetkin.
Joshua later tweeted footage of the incident and described Miller as a "lil pup barking" in the presence of "big cats".
Before the press conference started, an angry Miller took exception to being asked to take his seat, shouting: "I'll sit down when I feel like it, ain't nobody dictating to me. I starved off these streets, eat off these streets. I'm the underdog?
"Now, I will take my seat."
Once proceedings finally got under way, Joshua pulled no punches about the unbeaten Miller's credentials, saying the 300-pound slugger "punches like a fairy" and was the "softest puncher in the heavyweight division".
Joshua has stopped 21 of his 22 opponents, with only Kiwi Joseph Parker taking him the distance, and he vowed to knock out Miller in his own backyard.
"I'll be deadly serious. Jarrell can't beat me, not even on his best day," the big Brit said.
Miller, meanwhile, said he relished his underdog status and claimed Joshua didn't want to face him next, preferring an easier fight with British rival Dillian Whyte.
"He didn't want this fight first. He wanted easy money, Dillian Whyte. He has got to earn the right to eat at my table. This is the New York table", Miller said.
"He can be the pretty boy. I will still grind it out.
"I breathe, eat and sleep Anthony Joshua. I got a picture on my wall of Anthony Joshua. I wake up in the morning with Anthony Joshua.
"The way I got here is unconventional, something out of a fantasy book. I worked hard for this, hard. Ground it out. I got to go to war."
Earlier, Miller had told Sky Sports in the UK that he would make Joshua "crack like an egg" by coming forward and throwing a lot of punches.
"You can definitely expect [me to give Joshua a lot of problems]," Miller said "I know he knows what's coming. I don't know how much of it he can take.
"I guarantee it, you are going to see him crack like an egg. For sure. I know he's not prepared for [my size]. This is going to be bully season. He's bullied for all the right reasons. This is the boxing business, this is the hurt game, so ain't nothing humble about this or nothing nice about this game."