According to police, one of the suspects recorded the beating with a cell phone then posted it online.
All three teenagers were charged, and all remained behind bars Monday afternoon. They were being held without bond.
Police say the deadly videotaped beating took place in a Rogers Park alley in the 6300-block of North Artesian last Tuesday.
"Jones started his video recorder on his cell phone and stated, 'I think I'm gonna knock this guy out,'" said Cook County Assistant State's Attorney Terry Clancy.
Mora was collecting cans to help support his family at the time of the attack. Family members say he used to work in construction but had stopped working recently because of a workplace injury and health problems.
Investigators say the three suspects surrounded Mora before Malik Jones, 16, asked if he had any money. When the man didn't respond, Clancy says: "Defendant Jones asked him again if he had any money; defendant Jones then punched the victim in the jaw, and the victim then fell to the ground, the back of his head striking the cement."
In court, prosecutors said that the trio stole $60 from Mora and could be heard in the recording laughing about the attack as they fled.
A passerby found Mora hours later and he was taken to St. Francis Hospital in Evanston in critical condition. The Cook County medical examiner's office says Mora died Wednesday afternoon from blunt head trauma.
On Monday, prosecutors said that the teens were playing out a "game" they called "pick'em out, knock'em out" when they used a cellphone to record the deadly attack and then posted the video on the internet.
"I think they are heartless. Why they would do this to a guy, older guy, 62? You know, I don't know. It is so painful," said one of the victim's sons, Jose Mora.
One suspect, Malik Jones, 16, is charged as an adult, but police are not releasing his photo because of his age. Police say he delivered the punch that killed Mora.
Nicholas Ayala, 17, and 18-year-old Anthony Malcolm are also charged. Relatives of Malcolm said he is a good kid who had never been in trouble before.
"My brother is a good person. He goes to school, he gets good grades. He gots a job. He don't get into trouble. He just was at the wrong place with the wrong people," said sister Stephanie Malcolm.
"He wanted to be a FBI agent. This is his goal. Now he messed it all up, because he was hanging with the wrong crowd of people," said family friend Melvin Corhn.
"We would just like to send our condolences to the family; it's a sad situation, but my brother is not that type of person," said Jacovina Rodriguez, Malcolm's sister.
Investigators said that Jones handed one of his two alleged accomplices his cell phone before the attack and that the phone was used to capture the incident. The suspects posted the video of the deadly beating on Facebook.
A witness spotted the video on Jones' Facebook page and forwarded it to a second witness, who identified Jones as the person who battered him in a separate incident. Those witnesses contacted police, leading to the arrests.
One of Delfino Mora's children identified his father on the video for investigators.
"When he was on the ground, he was already unconscious. When he fell on the ground...his head bounced off the floor," Emmanuel Mora said.
Delfino Mora is being remembered as a loving husband and father to six boys and six girls. His family says he loved to play the guitar.
Relatives are now trying to plan funeral services and are gathering up money to return his body to Mexico. Family members say he had been working all his life to bring his children from Mexico to the United States.
Mora's relatives did not appear to be present for Monday's bond hearing.
All three defendants are due back in court in August.
(The Associated Press contributed to this report.)