Empty fruit cocktail, peaches, pineapple, and oranges out into a strainer set over a large bowl to drain.

Meanwhile, beat cream cheese in a bowl, adding milk until mixture is smooth and creamy. Mix in 3/4 of the whipped topping and 1/4 cup of the drained juice; blend well.

Dice peaches and fold them into the creamy mixture. Add all the drained fruits and coconut, reserving 5 or 6 mandarins, and stir to coat. Smooth over the top and frost with remaining whipped topping. Decorate top with reserved mandarins. Refrigerate until flavors combine.