The mysterious artist confirmed the piece, which appears to be a girl firing flowers into the air, by posting photos on Instagram.
He later uploaded a clip of the shredding online with the caption 'Going, going, gone.', with Sotheby's later confirming the prank had been staged by the artist.
Mr Simons' daughter, Kelly Woodruff, 37, told the Press Agency: "We've been down here all day and it's just been a complete buzz of excitement".
"My slight worry is, we've got this Storm Dennis coming on the weekend, so I really want to try and protect the roses", she added.
The work is expected to bring increased visitors and tourists to the Barton Hill area of Bristol, as people from around the world continue to visit the city where Banksy is from and where so many of his graffiti pieces are on display.
'We hope it's Banksy's work.
"Come and have a look yourself".
She also said the family were looking to get glass to cover the art to preserve it, but said Bristol City Council was unable to offer any help.
Banksy has not revealed any information about the mural, but the subject matter and the timing suggest a connection to Valentine's Day.
"Thank you for sharing your story #banksy", wrote @ShashanaBrown.
The footage features an interview with a man pictured stenciling a black insect onto a wall and painting a picture of a baby with blocks spelling "KILL MORE", both of which are pieces that have been attributed to Banksy previously. His eyes, eyebrows, and forehead could be seen.