Executive director Lisa Koch (COOK) says the animal group was called Wednesday by someone who spotted the black-and-white kitty in the city's northwest.
The tape was wrapped so tightly around the cat's legs and paws that it was cutting off circulation.
Koch says the feline has already undergone hours of emergency surgery to try to address tissue loss and infection.
A veterinary team is to decide Monday whether to amputate one of the animal's legs.
She says rescue officers have named the cat "Bruce Almighty" because of his will to live.
"He really had struggled to survive until they found him and, literally, he did collapse in their arms when they picked him up," Koch said.
Bruce Almighty even purred as his paws were freed from the bands.
"We're taking it one step at a time ... (and) hoping to save all four of his legs, but at this point in time, it's not looking good for one of his legs."
The humane society is asking anyone with information about what happened to please call.
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