A machining process and apparatus capable of increasing removal rates achievable when machining titanium and its alloys. The process includes heating a portion of a workpiece with a laser beam, cryogenically cooling a cutting tool with a cryogenic fluid without flowing the cryogenic fluid onto the workpiece, and machining the heated portion of the workpiece with the cutting tool. The apparatus includes a cutting tool, a device for heating a portion of a workpiece with a laser beam prior to being machined with the cutting tool, and a device for cryogenically cooling the cutting tool with a cryogenic fluid without flowing the cryogenic fluid onto the workpiece. The cryogenic fluid is circulated around the cutting tool to achieve a temperature differential between the workpiece and the cutting tool that is capable of improving removal rates and extending tool life at cutting speeds of, for example, above 100 m/min.