There are a lot of reasons why generally tree topping or stub cutting is considered a bad idea, the branches just grow back very fast and in large numbers and are considered weak points in the tree. You can see the picture of the large tree that was recently cut and the branches grew back again. The customer decided (after paying twice to be cut) just to remove the tree. The Mulberry trees still provide privacy and shade but they were getting too tall and blocking the sun from the whole yard and pool so they will require maintenance to keep them.