I have a dogwood tree that is covered with powdery mildew on the leaves. I have been treating it all summer and managed to keep it alive. As soon as new leaves come on the tree they get infected. Would it be OK to take off all the leaves with hopes that new ones coming out will not get infected??

A dogwood is like zinnias, as far as the watering/mildew reaction.
I have found overhead watering, especially with sprinklers will cause this. You want to water at the base of the tree, do not wet the leaves. This is true especially when evenings are cool.