I went to Bowling Green State University, and they have Freddie and Frieda Falcon:
http://bgsufalcons.collegesports.com/trads/bgsu-falcons.html
Freddie was introduced in 1950, and the female version of the mascot got her start in 1966 as Mrs. Freddie Falcon. Since then she’s morphed into Frieda, Freddie’s little sister (weird, I know), and the student inside the suit is female (Mrs. Freddie’s costume was piloted by a male cheerleader).
At the all-female academy I used to work at, the mascot was a jaguar, so gender neutral there.