PETA's imploring the Cleveland Browns to do away with their live-mascot tradition following the death of their sideline dog ... telling TMZ Sports it believes the practice is harmful to animals.
Tracy Reiman -- PETA's executive vice president -- made the urging on Tuesday afternoon ... just hours after the NFL org. revealed its bullmastiff mascot, Swagger Jr., had passed away at five years old.
Reiman said in a statement that "generations of breeding for a certain look have left bullmastiffs prone to hip dysplasia, cancer, and life-threatening heart issues, among other painful conditions.