The RSPCA and the Police Tri-Force Specialist Operations Collaboration said they were "extremely upset" by what had happened.
Tyson was one of 12 dogs successfully rehomed to various police forces from the Taunton area animal centre.
The outcome has devastated police dog handlers and RSPCA staff who cared for and trained the 18 month-old dark brindle and white dog.
Inspector Dave Eddy, who oversees the Tri-Force Dog Section, said: "We are absolutely devastated Tyson had to be returned to West Hatch, and that due to being a banned breed, he had to be put to sleep in accordance with Dangerous Dog Act.
"It can be very hard to identify the dangerous breeds if they are mixed with other breeds that look similar such as Staffordshire Bull Terriers.
"In Tyson's case, it was our expert Dog Legislation Officers who identified the physical traits.
"A number of our drug and explosive search dogs are rescue dogs and include Labradors, Springer Spaniels and Staffordshire Bull Terriers.
"PC Lee Webb who looked after Tyson was particularly upset. PC Webb already handles a rescue Staffie, PD Kos, who is an excellent search dog.
"We will continue to use rescue dogs and work with the RSPCA to use rescue dogs wherever possible."
An RSPCA spokesperson commented: "All of the staff who cared for and loved him are incredibly upset that such a wonderful dog had to be put to sleep."
They added: "Utimately poor Tyson illustrates the absurdity of the breed specific legislation and the Dangerous Dogs Act, and is another lovely dog who has paid the price because of it."
A spokesperson for the Department for Environment, Food and Rural Affairs commented: "The laws on prohibited type dogs are there to protect people from types of dogs bred for fighting.