A surgical device for cutting substantially across a cornea of an eye of a patient, the device including a positioning ring to be attached to an eye surrounding a cornea to be cut, and defining an aperture sized to receive and expose the cornea to be cut. The surgical device further includes a cutting head assembly structured to be guided and driven over an upper surface of the positioning ring in a generally arcuate path, and having a cutting element positioned therein and structured to oscillate laterally to facilitate smooth and effective cutting of the cornea. The cutting head assembly is structured to be detachably coupled to the positioning ring by a coupling member which permits movement of the cutting head assembly relative to the positioning ring along the generally arcuate path, but maintains sufficient engagement therebetween to ensure that smooth, steady, driven movement is maintained.