A method of removing material from a blood flow lumen includes providing a device having a cutting element and an opening, the cutting element being movable relative to the opening. The method then includes advancing the device through a patient's vascular system to the blood flow lumen. Finally, the method involves moving the cutting element and the opening relative to the blood flow lumen so that a continuous piece of material is severed by the cutting element and directed into the opening as the cutting element and opening move through the blood flow lumen, the continuous piece of severed material being directed into the device for removal from the patient. The method may include providing a device having a rotatable cutter that, in some embodiments, is not parallel to the longitudinal axis of the device, is movable, has retracted and deployed positions, or any combination thereof. The method may further include forcing the opening toward the wall of the vascular site after the advancing step and before the moving step.