Abstract: The device comprises a tool 21 with a cutting part 23 and a shaft 25. The shaft 25 is provided with an annular catch groove 25d and carries a sleeve 31 which encloses it and comprises a catch projection 31c which engages in the catch groove 25d so as to be detachable, wherein the shaft 25 and the sleeve 31 are rotatable relative to one another. The sleeve 31 is provided with a coolant inlet 31d which opens into an annular duct 41 enclosing the shaft 25 and communicating with a passage 43. This duct 41 is connected with the passage 43 for guiding a coolant, which passage 43 extends through the tool 21 until its cutting part 23 and opens into the surroundings at the free end of the cutting part 23 or in the vicinity of the latter. The sleeve 31 can be secured against axial displacements by means of a catch projection 31c, which is engaged in a catch groove 25d, without separate connection parts and without taking up much axial space.