Rescuers were next to Jones for much of the day but he was wedged in a small hole too tightly to pull him out or even reach through to assist him, Cannon told The Associated Press.
"Over the past several hours he was experiencing difficulty maintaining consciousness and breathing. With whatever other factors there were, he did not survive," Cannon said.
The 6-foot-tall, 190-pound spelunker got stuck with his head at an angle below his feet about 9 p.m. MST Tuesday. At times more than 50 rescuers were involved in trying to free him.
The crevice where Jones was trapped was about 150 feet below ground in an L-shaped area of the cave known as "Bob's Push," which is only about 18 inches wide and 10 inches high, Cannon said.
The process was slow throughout the day Wednesday with rescuers chipping away with air-powered tools in the narrow tunnel.
At one point late in the afternoon, Jones was freed from the crevice, only to fall back several feet into the tight space when a cord that was supporting him failed, Cannon said
Rescuers were able to get him food and water during that temporary freedom.
"They were right there with him, checking his vital signs," Cannon said. "They were able to get close enough to verify that he was deceased."
He said crews had suspended efforts to free his body for the night, but would resume at first light.
Jones, a medical student at the University of Virginia, was part of a group of 11 people exploring the cave passages.
"We were just looking forward to a good time," Mike Jones, the victim's 32-year-old brother, told The Salt Lake Tribune.
The group split up, with several children and some adults staying in a less dangerous area of the cave while others decided to explore further, 23-year-old Josh Jones, another brother, told The Salt Lake Tribune.
"It basically got to a point where we were trying to figure out if the cave went any further, and that's the route John decided to take," 25-year-old Joey Stocking of Logan told the Tribune.
Jones was going head-first into the crevice when he got stuck.
"He thought he could kind of keep going on his belly down further, but it got to point where he couldn't go any further and he got wedged in," Stocking said.
The group tried to free him.
"I was only able to see his two feet that was hanging there in the crevice," Josh Jones said. "I wasn't able to see more because he was engulfed in the crevice itself."
Nutty Putty cave is actually a hole on the top of hill about seven miles west of State Road 68. The naturally formed thermal cave is about 1,500 feet long. Its multiple, tunnels and passageways lead to room-like openings, a Web site for Utah cave-enthusiasts explains.
According to the official Nutty Putty cave Web site, the area was first discovered in 1960. The cave is privately owned by Utah's State Institutional Trust Land Administration. An access pass is required to explore the cave, with usage restricted to about six groups daily.
The county's last rescue there was in 2004.
Cannon said officials considered closing the tunnel or sealing it off after the last rescue but ultimately decided to erect a gate that requires a key for entry.
"We've had people stuck in this exact same spot. We're working and working to get him undone out of the spot and we don't really have any way of predicting what's gonna happen until -- boom, all the sudden they're out," he said.