Using a long serrated knife or bread knife, slice angel food cake into 3 equal horizontal layers. Place the bottom layer onto a freezer-proof plate.
Remove packaging from the ice cream and slice about 1-inch thick. Working quickly, place ice cream slices on the bottom cake layer, filling the gaps with ice cream and leaving the center unfilled. Lightly press the ice cream pieces together to form a solid layer the same size as the cake layer. Repeat with the second cake layer and remaining ice cream. Top with the final layer of cake and freeze until the ice cream is firm again, about 1 hour.
Frost the entire cake with whipped topping. Garnish with fresh strawberry slices and mint. Serve immediately.