Abstract: A tool for removing a disk or cylindrical core from a workpiece which includes a shank, an extension piece and cutting elements, the extension piece being in the form of a hollow cylinder and including apertures in the wall thereof for the introduction therein of a coolant. An axially movable centering element is positioned with the extension piece, the centering element including a centering spigot which fits into a cup-shaped centering piston, plate springs within the piston and against which the centering spigot is movable, and an elastic ring therearound for contact against the inner wall of the hollow cylinder.