An indirect cooling system for a rotating cutting tool uses a cryogenic coolant that is delivered to a cavity formed on the back surface of the cutting element, providing cooling near the cutting edge of the element. Because the total flow rate of the working fluid is low (less than 0.08 Liters/min/cutting edge), the fluid can be safely vented to atmosphere from the cavity, and as a result, no specialized coolant recovery or ventilation equipment is needed. The cavity may be formed with fins to enhance the heat transfer between the cutting element and the coolant, and coolant may additionally be sprayed directly onto the exterior surface of the element to cool the tool-chip interface. The indirect cooling system may be used for hard to machine metals and composites, as well as the machining of conventional materials without the use of traditional cutting fluids.