An officer found the dog in the village of Wintersett, near Wakefield, on Tuesday.
It had injuries that police believe were sustained through dog fighting.
In a statement posted on Facebook, the West Yorkshire Police Wildlife and Rural crime unit said: "As many of you will know all the force wildlife officers are volunteers and do it on top of their other duties.
"Yesterday PCSO Starford from Wakefield came in on his day off to locate a dog that had been found deceased.
"The dog was a Staffordshire Bull Terrier type and had injuries consistent with having been involved in dog fighting.
"If you were in the area of the bridge over the old railway line, at Wintersett, Wakefield, over the weekend and saw anyone dumping something or parked in a strange place please call 101 and quote 13210631380."