Anthony Waters, 42, suffered a lacerated spleen and broken ribs during the attack Wednesday night and died at a hospital, police said.
"The pack mentality going on in the city of Cleveland must end," police Commander Calvin Williams said Thursday at a news conference where he urged the attackers to come forward.
Portions of the attack were caught on a surveillance camera outside a towing company on the city's east side. Police said the videotape shows passing cars slowing to watch three teens attack Waters until he staggered into the parking lot, where he was assisted by employees of the towing company.
"It was just horrifying the way he looked," said Marlo Massey, Waters' sister, who saw her brother's body after the attack. "They beat him to death and I just can't stop thinking what was on his mind while it was happening."
Waters suffered from blunt abdominal trauma, a head injury and damaged internal organs, the Cuyahoga County coroner said.
The attackers, who appeared to be between the ages of 14 to 17, robbed Waters of a music player and headphones, police said. No arrests have been made.
Waters was a welder by trade but had been staying at a Cleveland-area homeless shelter, said Paul Eadeh, a friend.
"He's a good guy, a hardworking person," Eadeh said. "He was just trying to make some money to eat and to live."
Eadeh said Waters worked odd jobs for him at a beverage store.