The reinforced concrete chimneys which are more than 200ft tall make up part of Polmadie waste site which is being transformed into a £154million recycling and renewable energy centre.
They are being "nibbled" down over the next three weeks by a 250-tonne long-reach excavator which is more than 230ft at its highest point.
New tough environmental controls have meant Polmadie was latterly used for recycling, parking, administration and workshops.
The new Glasgow Recycling and Renewable Energy Centre will be able to handle 200,000 tonnes of council green bin waste from across the city.
Waste which can be recycled will be removed, organic material like food and garden cuttings will go into a plant which turns them into natural gas used to power the plant, with the remainder used to produce gas to generate electricity.
The new centre will save the city council around £254m over 25 years in expensive landfill charges.
It will bring more than 250 jobs to the city, support apprenticeships and will produce enough energy to power 22,000 households.
Once complete, it will deliver a saving to Glasgow of 90,000 tonnes of CO2 every year.
The development of the site is being carried out by Viridor, the UK's largest recycler.
Council leader Gordon Matheson, who helped start the demolition, said: "This is a hugely innovative project and an important step in the journey to deliver a more sustainable Glasgow.
"This partnership will not only produce enough energy to power more than 20,000 homes but will create skilled jobs and support apprenticeships that are vital to the city's economy.
"It is our opportunity to secure a future that is cleaner, more affordable and sees the city's waste work for the benefit of its people."