The Citizens United Against Cuts to Public Services group has told The Herald it has 30 volunteers ready to disrupt the planned demolition in an act of civil disobedience.
A resident of Barmulloch Road, who was sent a letter telling him he will have to leave his home during the event for safety reasons, has vowed to refuse.
The threats came as Shona Robison, the Commonwealth Games minister, backed the demolition as a bold and dramatic part of the opening ceremony. Her statement was the first from a Scottish minister on the plans.
"As part of the Games Strategic Group I believe the proposals symbolise a bold statement of intent on the power of the Games to be a catalyst for regeneration and positive change," the minister said. "For many people, these Games are more than sport, they are a chance for regeneration, renewal and having better places to live and work."
A petition against using the destruction of five of the six remaining Red Road towers as part of the ceremony has attracted more than 16,000 signatures.
Meanwhile, the family of Red Road architect Sam Bunton accused Glasgow 2014 chief executive David Grevemberg of "completely disingenuous conduct" after he insisted the towers would be brought down at the July 23 ceremony before of a meeting to discuss their concerns.
A letter from the family of Mr Bunton in The Herald today states: "The proposal is crass and appalling. Glasgow 2014 has to listen, and has to find a compromise. It is time for the Scottish Government to step in and show leadership."
Their actions are not connected, but both Mr Bunton's family and the protest group say the plan is tasteless.
One exclusion-zone resident, who asked not to be named as he fears a court order may be used to to shift him, said: "It's the biggest load of nonsense I've ever heard.
"They've said it will cause a 'wow factor' and we can watch it on the screens. I'm not interested in that and I'm not happy about them blowing them up for entertainment. How about building a memorial to all the boys who built them and died because of asbestos instead?"
Sean Clerkin, of the Citizens United group, insisted he was "deadly serious" about the plan to disrupt the demolition. "We'll be inside the exclusion zone," Mr Clerkin said, "and have people who won't be leaving their homes under any circumstances."
Glasgow 2014 has said it will not carry out the demolition unless it is safe to do so. A spokesman for GHA said it would work with partners, including the police, to ensure the public stick to the exclusion-zone boundaries.
In response to Mr Bunton's family, a Glasgow 2014 spokeswoman said: "We welcome the opportunity to discuss our plans at a meeting … At the meeting we will share more about the context and importance of Red Road's role within the ceremony."
First Minister Alex Salmond was first told of the plan to demolish the towers as part of the ceremony at a meeting in February, and raised no concerns.