The new organ is being built by an English firm that has been building pipe organs since Queen Victoria was on the throne.
Paul and Neil Daly, from Nicholson and Co, of Malvern, are on the cathedral site for five weeks to supervise the deconstruction, supported by a team of specially trained Kiwis.
Nicholsons plan to start work on the new organ in May and have the full installation completed by mid-2017.
The new organ has been designed to suit a variety of purposes and will be heard publicly 300 times a year in services and recitals.
Its pipes range in size from 32ft (9.75m) long - for the low sounds - to the size of a pencil.
A "donate a pipe" appeal is trying to raise a $1 million shortfall.