Place a 9-inch tube pan in the freezer. Tear cake into bite-sized pieces. Remove pan from freezer; arrange layer of cake pieces in bottom of pan. Working quickly, alternate scoops of mint chip and cherry vanilla to make next layer; press firmly into cake. Add a layer of cake pieces, then a second layer of ice cream scoops. Finish with layer of cake pieces. Press cake down firmly. Cover and freeze 6 hours or overnight.
Invert cake onto serving plate. Return to freezer until ready to serve. If desired, pipe whipped cream, placed in a pastry bag, around top and bottom edges of cake.