Tom Johnston House has been left derelict since August 2012 when the council moved to its new home in nearby Southbank Marina.
Work to raze the building to the ground is expected to be completed by the end of the year,.
The site is up for sale and council chiefs hope to attract a developer, with planning permission already granted earlier this year for a food store, petrol filling station and restaurant.
But residents are questioning whether the plans will benefit the town.
Some have slammed the move as a waste of money, while others want to see the land used to ease a lack of housing in the area,
On Facebook, Steven Moffat said: “Instead of affordable housing why not build council houses on the council land.
“They are always saying there’s a shortage due to the right to buy scheme. Now they have a chance to do something about it while they own the ground.”
Nick Gall added: “We don’t need another supermarket. We do, however, need genuinely affordable housing.”
Thomas Glen, director of development and regeneration, said: “The council moved its civic headquarters from Tom Johnston House to the Marina in August 2012, as part of the Corporate Asset Management Programme, to increase efficiency, reduce maintenance costs and achieve savings.
“At its meeting on 25 June 2015, the Council decided to proceed with the demolition of Tom Johnston House following completion of the tender process.
“As previously publicised, work is currently underway on the demolition of the derelict property and it is expected to be completed before Christmas.
“In April, councillors approved a planning permission in principle application for a mixed-use development - including a food store, petrol filling station, restaurant and associated parking - at the former Tom Johnston House site and neighbouring Whitegates Business Park.
“Both the Council and Sim Properties (Whitegates) Ltd still own their respective properties, but the 10-acre joint site is being marketed - potentially paving the way for a major boost for the local economy.”
Check out our video showing the start of the demolition at www.kirkintilloch-herald.co.uk