A device and surgical method for promoting suitable grafting between a healthy donor cornea button and a recipient's healthy corneal tissue. The device is a cornea transplanter comprising a cutting device, a support block having a removable base plate, and a vacuum device. The cornea transplanter is capable of retaining healthy donor corneal tissue as it is buttoned and placed onto the recipient's eye, with minimal physical manipulation of the donor corneal tissue. Once the cornea button is properly positioned, sutures may be symmetrically placed around the cornea button, using suture grooves that guide the suture needle to a particular depth and length of pass.