An intravascular catheter includes a flexible guide wire mounted for relative rotational and reciprocal movements within a reciprocal and flexible first tube or sheath. A rotary and flexible second tube is mounted for relative reciprocal movement on the first tube and has a rotary inner cutting head secured on an end thereof. The inner cutting head is closely fitted within an outer cutting head that is slidably mounted on the first tube. In carrying out the method of this invention, a blockage in a blood vessel, such as a coronary artery, is located and the outer cutting head engages the blockage to cut the blockage into fragments in response to rotation of the inner cutting head. The fragments are flushed-out from the inner cutting head and are drained through an evacuated annular passage defined between the first and second tubes.