A lateral incision catheter device is described which has a first shell formed as a hollow semi-spherical surface of hard, rigid material with circumference approximately that of half a true circle, and having a longitudinal axis longer or shorter than that of a true circle, and the shell edge on each side of the longitudinal axis being a cutting surface, and with a first catheter passing through and being bonded to the first shell on the longitudinal axis of the first shell near the distal end of the first catheter and a second shell essentially the same as the first but slightly larger and bonded to the distal end of a slightly larger catheter so as to surround the first and having an opening on the longitudinal axis for the distal end of first catheter to enter and thus serve as the axis for both concentric shells. A practitioner advances the lateral incision catheter to a pre-selected site in the lumen of a blood vessel, rotates one or both catheters to properly position the shells radially then rotates the first catheter and second catheter in opposite directions so the cutting surfaces of the shell edges engage adjacent tissue to cut out and remove a section of patient's lumen wall between the closing shell edges, and after the first and the second shells have rotated about 180 degrees they constitute a substantially closed container holding the excised portion of lumen wall which may be removed from the blood vessel by retraction of the lateral incision catheter. The device may be introduced through and used in a hemostatic guiding catheter which prevents blood from escaping though the opening on the lumen wall after the opening is made.