Paul Johnston says his three-year-old Maltese-poodle cross named Cooper was attacked during a hiking trip northwest of the city.
He says he jumped in to break up the fight and was tending to his severely injured dog when the other dog's owner left.
Bylaw officers are asking for more information about what happened at Mount Finlayson on Saturday.
The pit-bull cross is described as primarily white, with brown and black markings, and its owner is a man in his late 30s or early 40s with upper-body tattoos.
Johnston says he wants to see the dog put down before another attack can happen.
"It feels like I got punched in the stomach and that feeling isn't going away," he said. "Coop ... wouldn't hurt anybody. He deserves justice." (CFAX)