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.

Mrs Banda came to power two years ago after the sudden death of President Bingu wa Mutharika.
Her reputation has been dented by a corruption scandal, known as Cashgate, which has led donors to cut aid.
Her main challengers are Mr Mutharika's brother, Peter, Atupele Muluzi - the son of another former president - and a former preacher, Lazarus Chakwera.
By Chakuchanya  HarawaBBC Africa, Blantyre
Competitive election
Mr Chakwera is the candidate of the Malawi Congress Party, which governed from independence in 1964 until the first multi-party poll in 1994.
Voting was delayed in parts of the largest city, Blantyre, due to a shortage of election material.
"There's no ink. We're still waiting for the consignment," one of the officials told the crowd, reports the Reuters news agency.
There are reports of angry scenes at some polling stations.
But in the capital, Lilongwe, voting mostly started on time, Reuters reports.
Mrs Banda has denied any wrong-doing in relation to Cashgate and last week told the BBC that the fact the affair has gone to court was her "greatest achievement" because in the past, such scandals would have been covered up.
Scores of officials, including former ministers, have been arrested over the scandal, often with large amounts of cash. Up to $250m (Â£150m) may have been lost through allegedly fraudulent payments.
Analysts say that despite the close race, she is likely to win because of her popularity in rural areas.
The candidate with the most votes is declared the winner of the presidential race - there is no run-off.
There is a total of 12 presidential candidates.
Parliamentary and local elections are being held at the same time.
Malawi is one the poorest countries in the world and is heavily dependent on aid, with donors proving 40% of the budget.
A Londonderry recycling plant destroyed in a fire that began on Wednesday morning is being demolished.
[NEXT_CONCEPT]
Malawians have voted in a tight election, with President Joyce Banda facing three strong challengers.