African elephant females stand up to 2.6m tall and can weigh more than three tonnes.
Police, ambulance and the Fire Service were called to the zoo about 4.30pm yesterday after alerts that the elephant had attacked Dr Schofield.
Police later revised this assessment to say it had been a "tragic accident".
Reports suggested the elephant got a fright and wrapped its trunk around Dr Schofield, possibly to protect her, before crushing down on her.
About 6.30pm, Mila's former circus owner, Tony Ratcliffe, came to the gates of the zoo demanding entry.
Mr Ratcliffe said he was the only person who could control the elephant, whom he referred to as Jumbo.
"I need to see the elephant to know exactly what the situation is and what state she's in. Tomorrow will be too late."
Mr Ratcliffe and his brother, Robin, were denied entry.
Mr Ratcliffe told Radio New Zealand a life was "lost her life through ignorance of the elephant and its capabilities".
He questioned whether other zoos in New Zealand had the experts to deal with a situation like the one that lead to yesterday's tragedy.
"What you've got to realise is racing car drivers drive racing cars, and elephant handlers work elephants."
Mr Ratcliffe rejected the suggestion the elephant had struggled to come to terms with living in the zoo after life in the circus.
He said he never had any trouble with the animal.
"My children have grown up around her ... she's been a beautiful elephant. She's been messed around with by people who have no knowledge of them at all."
Dr Schofield was owner and director of the Franklin Zoo, where she had set up a charitable trust to take on exotic animals in need of new homes.
In 2006, she bought and retired the last circus lions in New Zealand.
The director of the animal rights organisation Safe NZ, Hans Kriek, spoke to Dr Schofield about Mila the day before her death.
He said she had been full of enthusiasm for Mila's future, hoping to eventually send her to live with other elephants in a bigger sanctuary.
"When Mila was Jumbo in the circus, she had a stereotypic behaviour, often swaying her head from side to side," Mr Kriek said.
"Wild ones don't do that. It's a sign they are not coping well with their captivity. It was my understanding that she improved a lot from going to the zoo."
Dr Schofield had been looking at a sanctuary in the United States to which Mila could go once she had recovered enough to be social.
Auckland Zoo senior vet Richard Jakob-Hoff said some of his colleagues had gone to Franklin to see if there was anything they could do to help.
"All I can say is how shocked I am, and I'm really thinking about her family and the staff who I know are going to be incredibly distraught."
A neighbour near the zoo, who did not want to be named, said Dr Schofield's death was "so unbelievably tragic".
"She was just such a lovely person - she loved those animals so much, especially Mila."
Dr Schofield lived at the zoo with her sister and elderly mother, and often slept with Mila in her enclosure when the elephant was troubled.
"She would have done anything for those animals... I can't believe this has happened."
Bruce Ireland worked with Dr Schofield for about three months when Mila arrived at Franklin Zoo, but lost his job because the zoo could not afford to keep him on.
Mr Ireland worked at Auckland Zoo for 27 years, 18 of them with its elephants, and said he was brought in because Dr Schofield had no experience dealing with elephants.
He said Mila showed aggressive and unsettled behaviour and he was concerned about the dangers that posed.
"You never went in with her... because she was just too dangerous. It was a case of there was one guy - Tony Ratcliffe - who could handle her, and he was the only one who could handle her."
A year ago, Dr Schofield told the Herald that Mila had been settling in well at Franklin.
"She is beautiful and she loves her team," she said.
"Mila has been in a circus for 30 years, shackled in a circus and since she has been here she has only showed signs of improvement - her attitudes, her happiness, activities, Mila is a joy to see. But we are getting her ready for a social situation."
Dr Schofield worked as a veterinarian in Australia and New Zealand before moving into sales and marketing in the animal health industry.
Her death is the second known case in New Zealand of a zookeeper being killed by an elephant.
In 1954 at Auckland Zoo, 65-year-old Frank Lane died when the elephant Jamuna swung her trunk, knocking him into a wall.
His death was judged to have been the result of an accident, rather than a deliberate attack, and Jamuna lived the rest of her life at the zoo without incident.
