It takes its inspiration from the Catholic Church's secretive branch, Opus Dei, made famous by the Da Vinci Code book and movie.
Tōtara trust board chair and cardiologist Jithendra Somaratne said the school respected church teachings but would not be governed by the Auckland Diocese.
"We're independent, so that's why we don't call ourselves a Catholic school."
Its opening comes amid debate over the Government's reintroduction of charter schools, which are independent or private schools funded by taxpayers.
They are championed by Associate Education Minister David Seymour, who has a $153 million chest of public money to spread their uptake.
Supporters believe the model gives parents more educational choice.
Critics believe it funnels taxpayer cash from public schools into private hands in a process lacking transparency.
That criticism intensified when a small group recently launched a hostile takeover bid to turn Kelston Boys' High School into a charter school.
Somaratne said Tōtara Point School brought more choice to parents.
It would be the first publicly funded school in New Zealand to offer the Cambridge Primary syllabus, which was previously accessible only to children at fee-paying private schools.
"We're going to be offering it in a way that gives parents the opportunity to have it without the price tag," he said.
The school would set up a mentoring system in which teachers regularly met every student one-on-one and would involve parents more deeply in their children's education.
"Finally, the school will use the Spalding Method, which is a multisensory language programme that teaches listening, speaking, spelling, reading and writing simultaneously."
The method was highly regarded, especially for helping students with learning difficulties, he said.
Epsom's central location was chosen to make the school accessible to families from "all parts of Auckland".
Somaratne said the school would uphold Catholic teachings by imbuing them into daily life and developing virtues such as "perseverance" and "fortitude".
Father Sam Fancourt, who was ordained into the Opus Dei prelature in Rome, would hold Mass at the school.
The founding families were also motivated by the teachings of St Josemaria Escriva, who established Opus Dei in 1928, Somaratne said.
Opus Dei is a Catholic faction not bound to a diocese or geographic area; its leaders report directly to the Pope.
Its priests are often seen as strict and conservative. Inspired by Escriva, some still wear a cilice - a spiked chain - and use a whip to create pain or personal discomfort as repentance and meditation.
The group has also been involved in controversies, including a lawsuit by a group of women in Argentina who claim Opus Dei trapped and exploited them.
Somaratne said the new school's founders had been "completely open" with potential parents about Escriva's inspiration for them.
Tōtara Point School's model differs significantly from the 238 state-integrated Catholic schools nationwide.
Catholic schools follow the New Zealand national curriculum and a specially designed religious studies programme.
NZ Catholic Education Office chief executive Kevin Shore said the church's education team had little to do with charter schools.
The country's Catholic bishops had signalled no interest in converting to charter schools.
"The reason we're so committed to the state-integrated [character school] model is that there are very clear protections around special character that don't exist under the charter school model," Shore said.
That included requiring a high percentage of teachers to be "special character" staff. In Catholic schools, that meant staff whose religious training was typically assessed by the local bishop.
Catholic primaries required 60% of staff to meet this character. Charter schools required only one, Shore said.
That was a "key difference" for parents to understand.
Catholic school students must also demonstrate a connection to the church, while charter schools must accept any student who doesn't object to the school's character.
James van Schie, Auckland Diocese general manager, said that, although the new school was independent, the founding families had made the church aware of their plans.
"The school has not opened yet, but the early days of our relationship is warm and supportive, we expect this to grow over time.
"We don't see this school as a competitor."
Somaratne agreed, saying the "thriving" Epsom Catholic primaries with full rolls served their local parishes.
His school, however, brought choice and marked a "new chapter in education".
To symbolise that, he said, the parents had incorporated Tōtara Point in their school's name because it was the location of the first Mass held in New Zealand.