Environmentalists are calling for a public inquiry into the salvage operation following the grounding of the coaster RMS Mulheim near Land's End.
The jack-up rig is to be removed
Surfers Against Sewage (SAS) say the operation was badly handled.
The Maritime and Coastguard Agency (MCA), which is co-ordinating the operation, has admitted it may take weeks to remove the vessel's cargo.
The Mulheim was carrying 2,200 tonnes of shredded plastic when she ran aground between Sennen Cove and Land's End on 22 March.
Salvors are bagging the waste and hauling it up the cliff after a jack-up rig alongside the vessel was damaged by the sea.
We now have a second wreck, which is the salvage equipment itself
Richard Hardy, Surfers Against Sewage
On Sunday they moved 10 tonnes, and 20-30 tonnes on Monday.
Meanwhile, tonnes of the plastic cargo has been washed from the ship through a hole in the hull.
SAS campaigns assistant Richard Hardy said: "It's been three weeks since the Mulheim came ashore and we have seen very little to convince us that the operation is going very well.
"It's been a massive environmental disaster.
"And we now have a second wreck, which is the salvage equipment itself."
He added: "We need to make sure that what has gone wrong is corrected so we can put in place a plan of action for something that could be a bit bigger in the future.
"Something like the Prestige could be just around the corner for us and we want to know that we can cope with that kind of disaster."
Mike Deeming, from the MCA, said the rig would be moved as "soon as conditions permit".
He said: "As far as I am concerned, we are concentrating on the job in hand. We are doing that to the best of our ability."
The coastal path has been diverted, but environmentalists have raised concerns that ground-nesting birds, such as skylarks, near the site could be endangered by tourists who have been gathering to see the wreck.
Joe Oliver, area warden for the National Trust, said: "They abandon their nests if they are disturbed by people and dogs.
"It's also a fantastic habitat for lizards, slow worms and adders, so we would advise people to keep to the paths."