A rotatable cutting tool includes a rotatable tool body and a replaceable cutting tip for chip removing machining. The tool body includes a forward free end having a first dovetail coupling part formed thereon. The cutting tip includes a front cutting end and a rear mounting end. The mounting end includes a second dovetail coupling part joined to the first dovetail coupling part. An actuator, such as a screw, is provided which is arranged for elastically deforming one of the dovetail coupling parts to create a tightly clamped relationship between the first and second dovetail coupling parts. Insertion of a replacement cutting tip is performed by laterally mating the dovetail coupling parts until one of the coupling parts abuts a laterally facing stop surface of the other coupling part.