Experts decided sections of the famous building had to be demolished on safety grounds after flames tore through the Charles Rennie Mackintosh-designed art school on the night of Friday June 15.
The fire, which spread to nearby properties including the O2 ABC, came amid a major restoration project inside the Mackintosh building following a large fire in 2014.
Structural engineers David Narro Associates and contractor Reigart drew up a detailed plan for the work which includes dismantling areas “brick by brick” with removed parts to be moved into storage.
Unstable masonry on the south side of the building was the first to be removed on Tuesday, with the work expected to take several weeks.
Dominic Echlin, of David Narro Associates, said: “The primary aim of the initial works is to make the building safe and structurally stable.
“It is important to understand that our agreed approach is the safest way to dismantle the dangerous elements of the building and, importantly, ensure there is no damage to nearby properties or risk to those working on site.
“The contractor is starting today to reduce the height of the high level walls on the south side of the building, carefully taking down damaged and unstable masonry.
“With the machinery brought to site the contractor can work on several ‘fronts’, so after a start today in the middle of the south facade, we will quickly move on to reducing height to the top parts of the south-east corner and east facade. Work will then follow on the west end and then parts of north facade.
“This sequence has been determined so we keep the building as stable as possible and the dismantling controlled throughout the process.”
Four further cranes are expected to be moved to the site to support the work.
The art school said Glasgow City Council Building Standards will assess whether it is possible to reduce the size of the exclusion cordon around the building as the dismantling progresses.