From a Daily Universe article:

In 1926 the two “somewhat tame” cougars, named Cleo and Tarbo, were released on the floor during a dance at the Women’s Gymnasium, resulting in “some panic” (p. 123).

According to the BYU Athletics website, “live cougars prowled the sidelines of BYU games on a regular basis through the late 1940s and on special occasions through the 1960s.” After Cosmo appeared on the scene in 1953, there were occasions when he and his wild four-pawed cousins shared the sidelines; but, in the end, the bipedal mascot stood the test of time. In 1979, when “students tried to bring back a live cougar mascot at athletic events,” BYU’s YFacts says, “school officials felt a student dressed in a cougar outfit would be a better (cleaner and safer) mascot.”