A system, apparatus and method for harvesting from the eye of a mammilian (e.g., cadaveric) donor a disc-shaped graft or lenticle consisting of corneal tissue and a quantity of scleral or pericorneal tissue wherein limbal stem cells are located. This graft or lenticle is then transplanted onto the eye of a human or veterinary patient to treat a disorder caused by the absence or deficiency of limbal stem cells in the patient's eye. The system of the present invention comprises a) an eye-contacting ring and cutter guide apparatus and b) a cutter apparatus. The eye-contacting ring and cutter guide apparatus is initially placed in contact with the donor eye such that a portion of the cornea and adjacent scleral or pericorneal tissue containing limbal stem cells protrudes upwardly through the center of the ring. The cutter is then engaged with guide member(s) formed on the ring and the cutter is advanced, severing the protruding cornea and stem-cell-containing pericorneal tissue. In this manner the desired lenticle is obtained for subsequent transplantation.