The present invention provides an atherectomy catheter which has a cutting element that is able to cut both soft tissue and hard tissue, and methods of cutting material from a blood vessel lumen using a rotating cutting element. The cutting element has a sharp cutting edge that surrounds a cup-shaped surface and at least one surface of abrasive material. The cup-shaped surface directs the cut material into a tissue chamber. The cutting edge and the cup-shaped surface together are well suited to cut and remove relatively soft tissue from the blood vessel. The abrasive material surface in combination with the cutting element is well suited to abrade and remove hard material from the blood vessel.