You can cut them down with no ill effects on them...but spider mites can be pretty well controlled with just a strong spray of water..just spray at them with a hard stream of water from your hose and most of them will be gone.
There are new varieties on the market now that are very mildew resistant...I like them so much that I pulled out all of my older varieties and just have the newer ones now..nothing looks as bad as a plant covered in mildew!