Firefighters have been tackling a major blaze at the building on the Electra Road in Campsie for more than three days.
The fire has burnt out enough to allow contracts to dismantle the building, owned by River Ridge Recycling.
The Northern Ireland Fire and Rescue Service (NIFRS) is still investigating the cause of the blaze.
Hundreds of tonnes of industrial waste was inside the building, and the fire service said the intensity of the fire made it difficult to deal with.
Eleven appliances are at the site and the operation is expected to continue into the weekend.
A NIFRS spokesman said: "Demolition has begun on site by contractors who are removing the roof and external panels of the building.
"This will give firefighters better access to the seat of the fire to continue to extinguish the fire."
Residents in nearby houses have been advised to keep windows and doors closed due to the smoke plume coming from the fire.
"Windy conditions remain on the weather forecast and people need to be vigilant to a change in wind direction, keeping windows and doors closed," the spokesman added.
Road closures near the site remain in place.
A Londonderry recycling plant destroyed in a fire that began on Wednesday morning is being demolished.