A cutter (8) is telescopically received in a cannula (9) and both the cutter and cannula are telescopically mounted on a tubular carrier (7). A detection device (6) may be inserted through the open-ended carrier, cutter and cannula to properly place the surgical instrument in alignment with the tumor to be excised. Positioning tines (80) may penetrate the patient to firmly locate the carrier in its proper position on the patient. The cutter and cannula are moved about the carrier and are pressed into the tissue of the patient with the expectation that the circular core (60) of breast tissue formed by the cutter will have clear margins about the tumor. If the tumor extends too close to the circular incision, the cannula may be rotated so that its sidewall opening (26) faces the side of the remaining tissue to be excised and the surgeon can pull the remaining tissue through the sidewall and excise it, thereby avoiding a separate and delayed surgical procedure.