Using a bread knife, slice the angel food cake into three layers. (I've used both store-bought & baked-from-a-mix.)
Spread whipped topping over bottom layer, then layer on half of the pineapple. Repeat for second layer, then put top layer in place.
"Ice" the entire cake with the rest of the whipped topping. Depending on how big your cake was, and how much topping you used for the layers, you may need to use part of a second container of whipped topping. This recipe could be made using "light" whipped topping to cut some calories, if you wish.
Decorate the top and sides of the cake with mandarin orange slices. Serve right away or chill first. Store, covered, in refrigerator.