However, neighbours of the school are lamenting the loss of the mature hardwood.
Arthur Street North Neighbourhood Support spokeswoman Liz Angelo said she was alarmed to hear chainsaws in the pouring rain on Wednesday when the work began this week.
Mrs Angelo lives in an apartment block across the street from the school and said the tree being removed served as a screen between the school and the apartment and it attracted tui that stopped passersby.
To her eye the tree had been "perfectly healthy".
During public meetings about the rebuild under way at the school months ago, she brought up her concern that trees at the site could be lost, she said.
Now, despite assurances from the ministry nearby trees would remain, Mrs Angelo was concerned the city was losing valuable greenery in the Town Belt.
In her 11 years in the city significant trees had been taken out, she said.
Her neighbour Ron Esplin said as a Kaikorai School pupil in 1952 he watched the trees at Arthur Street School being planted.
"This week in a matter of minutes, as a septuagenarian, I watched one of the oldest fall to the ground.
"The gaping hole has revealed to us regimented buildings, and to the children, their structured urban environment.
"How soon will I again witness the planting of saplings to seal this needless gash?"
Ministry of Education head of property Sam Fowler said the arborist work under way was not related to the school rebuild programme.
"A large wattle tree has exceeded its lifespan and arborists recommended to the school it should be removed for safety reasons.
"Other trees are being pruned as part of these works."
