Witnesses said the truck driver was not aware of the accident and stopped 70m down the road only after hearing the toots from other motorists.
Inspector Cornelius Klussein said that at the time the truck driver had the green light as he drove through the busy intersection.
Brendon Judd, who works almost directly above the crash site and was one of the first people to respond, said that by the time he ran out to check on Mr Tangiia it was clear he could not be saved.
The KiwiRail senior systems and standards adviser, who has experience dealing with pedestrian rail trauma, sprang into action moments after the collision.
"We heard some horns tooting. The first truck that the cyclist was struck by was being followed by another truck and he was tooting his horn trying to get the attention of the first truck driver. I looked out and saw the cyclist lying on the ground, and by the way he was lying I knew he was in trouble."
Mr Judd called 111 and ran for the street.
"When I got to him there was no pulse, there was no breathing ... There were absolutely no vital signs whatsoever."
Mr Judd praised three "young ladies" who helped shield the prone cyclist from crawling traffic.
"They were obviously very shaken [but] I asked if anyone had a blanket or something to cover him. When I looked back up they had a sheet up to shield the body. I think people were generally shocked but there was no hysteria."
The driver of the second truck, who witnessed the whole incident, was badly affected by what he saw, Mr Judd said. "I was concerned for the truck driver witness who saw it all. I asked if he was okay. He said, 'Nah, mate, I'm a bit shaken up.' He'd seen the whole thing and obviously it must have been pretty horrible to see."
Read more: Cycle advocates fear more deaths unless danger zones bypassed
Truckie left 'distraught' after death
The driver of a freight truck that collided with a cyclist in Auckland was "distraught" after the accident.
The father of five was unaware 37-year-old John Tangiia had gone under his wheels until he was alerted by another truckie honking his horn.
It is thought Mr Tangiia had been riding down Parnell Rise and turning left into Stanley St when he went under the truck, which was travelling straight through the intersection from The Strand.
Initial police indications were that the truck driver had the green light.
Mike Satherley, general manager of PBT Bulk, said the truck driver was a contractor with his own truck unit.
"The driver didn't actually see anything. He didn't even know," he said of the collision.
The driver, in his late 40s, had been rocked by the incident.
"It's not an easy thing to deal with. He's cut up, he's a family man with five kids. He's still feeling it, but he's managing okay."
Brendon Judd, a witness, said the truck driver was visibly upset when interviewed by police.
"I could see he was obviously distraught."
Auckland a 'nightmare' for bike users
A cyclist who dodged death during a horror smash 21 years ago says Auckland is a "nightmare" for bike users.
"You're taking your life in your own hands at some times," said Fraser Sharp, who was left brain-damaged with his promising athletic career in tatters after being mowed down on his bike in April 1993.
He says he was sickened to read about the death of John Tangiia, 37, who was run over by a truck at a busy intersection in Auckland on Tuesday.
"I don't know all the facts about this crash, but it's totally dreadful," Mr Sharp said.
"Auckland is a highly populated city and riding there is bit of a nightmare.
"Riders need to think about what time they go out, what routes they ride, and always respect motorists.
He said the death again highlights the need for both motorists and cyclists to take care on the roads - and to respect each other.
The 38-year-old has lived in France, where he says motorists show far greater respect for peddlers.
"So much more so than here," he said.
Mr Sharp is training for the Auckland 70.3 Ironman where he will raise cash for Brake, the road safety charity in support of people bereaved and seriously injured in road crashes.