Well, clutches are specifically designed to engage when engine RPMs increase. It sounds to me like simply lowering your idle speed will make it work properly again.
For a harbor freight 6.5, stand behind the engine at look at the carburetor... near the top of the carb (not air box) you should see a little black plastic flap (the throttle butterfly) that can pivot, and has a wire on it coming from the throttle assembly... there should also be a plastic screw on your side of that butterfly that the throttle butterfly sits against when it's not being pulled open, so it stays open a bit to idle. Mine had a round cover that I had to pop off with a knife to expose a phillips socket on the head... barely took any force, knife was just to dig in a bit and get a grip. Back this screw out (counterclockwise) to lower the idle speed.