In a bowl, combine raspberry gelatin and 1-1/4 cups of applesauce. In another bowl, combine lime gelatin and remaining applesauce.
Place three graham crackers side by side on a serving plate. Cover with a third of raspberry applesauce. Top with three more crackers and a third of lime applesauce. Repeat layers twice; top with remaining crackers.
Frost the top and sides with whipped topping. Refrigerate overnight. Cut into 1/2-in. slices.