A rotary cutting tool with a shank and an interchangeable cutting tip, wherein the shank includes a pocket which receives the interchangeable cutting tip via an interference fit. The pocket includes two centering wall portions which, when viewed along a central longitudinal axis, are oriented at a first angle with respect to one another, the first angle being greater than zero. The interchangeable cutting tip is axially displaceable between: an initial position, assumed upon being received in the pocket of the shank; a clamped position, wherein the interchangeable cutting tip is fixedly held with respect to the shank; and a bump-off position, wherein the interchangeable cutting tip is not fixedly held. A holding element holds the interchangeable cutting tip in the clamped position, and a bump-off element displaces the interchangeable cutting tip between the clamped position and the bump-off position. Other variants and embodiments are broadly contemplated herein.