A device for cooling and lubricating a tool during a chip removal machining process, which includes: a first subsystem for cryogenic cooling that includes: a first entry configured to introduce CO2 in liquid state in a first conduit of the device; a first exit configured to supply CO2 in liquid state from a second conduit of the device; a third conduit located between the first and second conduit; and means for preventing the formation of dry ice in the first, second and third conduits; and a second subsystem for lubrication that includes means for supplying micro-particles of a cutting oil in liquid state; wherein the first subsystem and second subsystem are independent from each other, and wherein the first subsystem and second subsystem are configured to act either simultaneously or either one alone. Method of operation of the device.