Copied from: https://www.gardeningknowhow.com/ornamental/trees/fruitless-mulberry/how-to-prune-a-mulberry-tree.htm
If pollarding, pollard to the knob, leave no more than 1cm, don't cut into the knob, pollard in the spring when it will stay above 50F and before the buds turn green (maybe late February in California, averages mid fifties).
Mullberry fruit grows on the previous years growth, if you want mulberries leave some of the previous years growth.
How to Prune a Mulberry Tree If you are wondering how to prune a mulberry tree, start with sharp, clean tools. Do not struggle while cutting through a branch. If this happens, your tool is too small. Use a hand pruner for cuts under 6 inches (15 cm.) and loppers for cuts 1 to 2 inches (2.5-5 cm.). You can also use a good saw for cuts 1 inch (2.5 cm.) and larger. Try not to cut branches larger than 2 inches (2.5 cm.) in diameter. Mulberry trimming should not be done on large branches unless you accept the fact that large wounds don’t heal very quickly and leave open the door for pests, disease, and heart rot. Pruning trees in pollard form should be started when the tree is quite young and the scaffold branches have grown to the height you wish for in the canopy. Always cut the smaller branches back to their base on the scaffold. A round callused knob will form over the years. Always cut to the knob but not into it. Do not leave a stub that is more than ½ inch (1 cm.) at the knob. Do some research on pollarding before you cut the tree. If you inherit a large tree that was pollarded in the past but not maintained properly over the years, hire a certified arborist to get it back into shape. When to Prune Mulberries Mulberry tree pruning is easiest when the tree is dormant. You can see the structure of the tree without it being obscured by leaves. Don’t prune when the weather is very cold. When the temperature is under 50 degrees F. (10 C.), it is harder for the tree to seal off its wounds. A good time for mulberry trimming is in spring prior to the buds turning green.