People flocked to see the carcass of the Southern Right whale at Mnandi Beach where children jumped on it, kicked it and one person hacked off bits of flesh from it on Wednesday.
People posed in front of it for photographs and two men climbed onto the dead animal to film the hole in its head left by the explosives used to kill it.
Pat Stacey, of Marine and Coastal Management (MCM), said: "It's unbelievable. People are all over it. There was even one person who cut pieces of flesh out of it. We're trying to keep them away."
About 30 children were rolling over the whale and "skiing" down its back.
The Southern Right whale, which beached on Tuesday afternoon, was put down on Wednesday after attempts to refloat it failed.
Mike Meyer from MCM, in consultation with whale specialist Peter Best, local authorities and Nan Rice of the Dolphin Action and Protection Group, decided that the most humane option would be to use explosives.
Police from the explosives unit used a cone-pack explosive device, designed to force the charge in one direction only. It was detonated over the whale's brain, causing immediate death.
Claire McKinnon, head of the city's cleansing department, said all animal carcasses had to be disposed of at the Vissershok hazardous waste site.
She said the council would use three front-end loaders on Thursday to roll the carcass along the beach to a spot where a flatbed truck was waiting. The 11-ton animal would be hoisted onto it by crane and taken to the dump.
She said the beach would not be closed to the public as the carcass did not pose a health risk at this stage.
Before the whale was killed, Meyer explained to the hundreds of curious onlookers over a public address system why the animal had to be put down and how they would do it. He explained it was impossible to refloat the whale.
Best said the whale was probably between two and five years old. He took skin samples to identify its sex. It was not possible to explain why the whale had beached itself.
Rice said she was "fed up" with the public interfering with whale strandings.
"They obstruct everyone's work. I'm also fed up with all the calls I get to complain about killing the whale," Rice said.
"There is no way anyone could have got the whale back into the sea.
"Using explosives is an internationally recognised humane way of killing stranded animals. You can't leave the thing baking in the sun for days, dying slowly."