The artist secretly built a shredder into the frame of Girl with Balloon, which self-destructed moments after it was sold for £860,000 at the auction.
An unnamed collector bought the piece which, including a buyer's premium, cost £1m.
Banksy implied that the stunt went wrong in a new video posted to his website.
The footage shows how a button was pressed to trigger an alarm from the painting, as part of it was sliced into strips.
A stunned crowd gasped and looked on and the painting was swiftly removed.
Part of the piece remained within the frame and was not destroyed.
"In rehearsals it worked every time..." a caption in the video notes.
Viewers are then shown a clip where an artwork was completely shredded, leaving the frame wholly empty.
Banksy previously claimed that preparations for the stunt were carried out "a few years ago" in case it was ever put up for auction.
The artist defended the shredding with a quote from Picasso: “The urge to destroy is also a creative urge.”
Sotheby's said the artwork has been given a new title, Love is in the Bin and that it has been granted a certificate by Banksy's authentication body.
The woman who bought the piece at the auction went ahead with the purchase.
"When the hammer came down last week and the work was shredded, I was at first shocked, but gradually I began to realise that I would end up with my own piece of art history," the buyer said, according to Sotheby's.
Alex Branczik, head of contemporary art for Europe at the auction house, said the piece was "the first artwork in history to have been created live during an auction".
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