It was a sightseeing flight that went terribly wrong and which still attracts conspiracy theories today.
But the search and recovery of the bodies became the template for all subsequent air disaster recoveries, from the 1988 Lockerbie bombing to the shocking crash of the Malaysian Airlines plane shot down over Ukraine last year.
Mitchell was immediately aware of the significance of the Erebus crash. On Nov 28 1979, he was an inspector in the New Zealand police force and a specialist in search and rescue. He had, by chance, spent the day teaching a course on victim identification, before heading off to an early Christmas party.
"I had just got home and was sitting down to dinner when the phone went. It was my boss, who told me I had better come in. At the time it was the fourth-largest air disaster in history, and I knew straight away this was going to be a biggie."
In New Zealand, search, rescue and recovery of bodies is a police job. The fact that the plane had crashed 2,500 miles away in one of the most inhospitable areas on the planet was not relevant. The plane was an Air New Zealand DC10 and the great majority of the passengers were Kiwis. Mitchell had just a few hours to gather a small team of policeman together, collect some cold weather kit from a Polar expedition base, and fly to Antarctica on a Hercules.
"I was quite keen to go," he says, speaking from his flat in Kent, having retired to Britain a few years ago.
"It was an opportunity to put into practice all that we had learnt. I suppose I was crazy."
His mission, and the tales of his team, are recounted in a riveting new documentary film Erebus: Into the Unknown, released in the UK this week, which splices their memories with dramatic recreations of the fortnight they spent on the glacier.
The scattered burnt wreckage of the Air New Zealand DC-10 lying on the snow-covered slopes of Mt Erebus 35 years ago.
While Mitchell comes across as a level-headed leader, many of his team were overwhelmed by the scenes of death and destruction they encountered. Stuart Leighton was just 22 at the time, and Mitchell said, in retrospect, he was probably too young to be part of the mission.
Leighton says in the film: "We had no idea what Antarctica would throw at us. We just knew it would be dangerous."
Even for the experienced policemen, the scale and the freezing temperatures were something they had never encountered. Leighton recalls: "There was a lot of mutilation with a lot of the bodies. It was grotesque. It was overwhelming. I personally felt a little bit out of my depth. I had the thought; 'I don't belong here. This is for the big boys."'
The team leader's main concern was not the sight of corpses scattered across the glacier, but his team's safety.
"The bodies didn't bother me a great deal because it goes with the territory," he said.
His biggest dilemmas were how they would cope with the sudden winds that hurled bits of metallic debris like missiles across the site, how they would avoid falling into the numerous fissures in the ice and how they would be able to recover 257 corpses, bag them up and return them to the New Zealand mortuary to be identified before the ice runway at the McMurdo base camp melted.
Mitchell instituted an efficient system, dividing the crash site into a grid. Each corpse, or body part, was numbered according to who had found the victim and where they were found.
"I am a chess player. So I used the international correspondence chess method of numbering the grid of the crash site."
The former policeman remains a serious international chess player. And his method is still used at disaster sites. It helped the team back in New Zealand to match dental records and fingerprints with the passenger list.
After setting up the operation, he spent most of the fortnight at the McMurdo base camp - 70 miles from Mr Erebus. Meanwhile, his team slept in tents at the crash site itself. Every day they would laboriously pick through the wreckage, with the help of a team of mountaineers and photographers.
Viewers of the documentary are left in little doubt about how gruesome the job was. Mitchell said: "If anything, the film understates it. There is no easy way to deal with a body. You have to pick it up, put a label on it, and you have to handle it. You can't airbrush it.
The four New Zealand police officers who were part of the ice recovery team on Erebus who received the New Zealand Special Service Medal (Erebus) Inspector Stuart Leighton, left, Superintendent Bob Mitchell, Sergeant Mark Penn and Inspector Greg Gilpin. Photo NZPA / Ross Setford
And some of those bodies were very difficult to get to. "Some corpses had fallen down a ravine, as the burning engine had melted the glacier. Many were difficult to put into a standard body bag.
Leighton said: "These bodies were frozen solid. Whatever shape they landed in, that's what they froze into."All of the team remember the stench of the disaster.
Mitchell said: "The smell of kerosene - jet fuel - takes me straight back to Erebus. It's not that I get flashbacks, but I immediately remember."
There were other challenging aspects of the mission, not least the endless presence of loud and aggressive skua gulls, carrion-eating birds of the Antarctic. The team resorted to burying the bodies again under the snow, once they had been bagged up, to stop the birds getting to them. They were there for 14 days and never stopped working. The perpetual daylight of the South Pole meant that they worked around the clock, 12 hours on, 12 hours off, but never properly resting, nor escaping the tragedy, even when having a meal.
Leighton said: "We had one set of gloves while we were there. They were baked with the fatty human remains, the soot, the whatever, and you ended up having to use the same set of gloves to put food in your mouth."
It is perhaps unsurprising that the policeman, who was then just a young man, was mentally scarred by his work.
"I remember thinking, 'Oh my God. I hope this is not going to traumatise me. I hope this isn't going to completely screw me when I get back.' Because I knew it had the potential to do so. And unfortunately it did."
At the time there was no counselling provision for the team when they returned. He said he has spent most of his life trying to come to terms with that fortnight.
Mitchell, for his part, said he does not like to dwell on the past "but there needs to be an opportunity for people to unwind.
Stu Leighton's life has been stuffed up by the fact he did not get the full opportunity to let people know." Today, counselling for search and recovery teams is routine. For all the scars some of the team were left with, it was a successful mission. Of the victims, 213 were successfully identified.
The Royal Commission into the causes of the crash ruled in its initial finding that it was not pilot error, but rather errors by Air New Zealand in allowing sightseeing flights to fly too low and for changing the course of the flight, without telling the crew so the aircraft was re-routed by computer into the path of the mountain.
It proved a controversial conclusion and was challenged.
The police, however, were universally praised for their recovery mission. And Mitchell is clear that air crashes, and body recovery, will remain part and parcel of modern life, despite improvements in aviation design.
"The airliners are getting bigger and they still crash."
Sadly, as events of this week show, he is correct.
