An apparatus for creating revascularization channels in tissue, such as the myocardium of the heart, mechanically cuts the channels using a hand piece with easily removable cutting tip assemblies having angled, sharpened edges to allow rapid tip replacement. The cutting tip assembly has an inner needle within an outer hollow needle with each needle attached to the hand piece for independent rotation and axial movement. The inner needle may be hollow, or formed with a pointed tip, and may rotate counter to the outer needle to enhance gripping and storage of the tissue excised by the outer needle. The hand piece may attach a cylindrical magazine of cutting tip assemblies or one cutting tip assembly. The cutting tip assembly may be heated to provide thermal damage to the heart muscle during the creation of the channel, providing some of the advantages of the laser method of TMR.