There really is a tree called a fruit cocktail tree--it is a fruit tree that has had other fruits grafted on to it. You can't just graft any fruit together though. They must be like kinds, such as all citrus fruits. The pruning of these trees is not much different than the pruning of single fruit trees. The biggest difference is these trees are usually not as young as the single fruit trees when you buy them, which means the early pruning and training is probably already done. It's really about shaping them to maximize the sunlight allowed in to produce healthy branches that can bear the weight of the fruit. Most pruning of fruit cocktail trees should be done in the summer.
Plant a new fruit cocktail tree. It should be about 50 to 60 inches high. In the summer, cut the main trunk to just above the highest branch. Use sharp pruning sheers and make a clean cut. Never break off or twist off a branch to prune it.
Check the branches for overcrowding. Leave at least a foot between the major branches. Cut off the dead or weak ones to make room for the healthy branches. Cut off any branches that are too low to the ground. Remember, the fruit is going to pull the branches down, so the first branch should be at least 2 feet off the ground.
Cut back branches of a particular fruit if it is starting to dominate the tree. You need to keep the fruits balanced or one will take over and kill off the other fruits.
In the following years, you only need to control the height of the tree. You might want to keep it at around 7 feet tall so you can reach the fruit when it's ripe. Keep the upper inside part of the fruit cocktail tree free from crowding. This will block the sun from getting to the lower branches and they won't grow as well. Cut off any branches that die or look diseased.
Only cut branches that are going straight up, instead of out, in the winter. You will be better able to see them once the vegetation is off. Pruning a fruit cocktail tree in the winter opens it up for disease to set in, so you want to do as little as possible.