For new medical β titanium implants, the surface micro texture processing technology is a difficult problem. To solve this problem, a new method of ultrasonic elliptical vibration cutting (UEVC) is adopted in this paper. The mechanism of material removal in ultrasonic elliptical vibration cutting is explored for different cutting paths. By means of simulation and experimentation, the material removal mechanism of ultrasonic elliptical vibration cutting medical β titanium alloy is revealed with respect to the aspects of cutting deformation, stress distribution, force and thermal variation, and chip formation mechanism. The results show that: (1) The cutting temperature and cutting force in the UEVC process obey the law of periodic change, and the maximum point of cutting force appears ahead of the maximum point of cutting temperature. (2) The material removal process of UEVC is a “press–shear–pull” composite cutting process. The tool squeezes the material to form the chips. Under the action of high temperature, the material is removed by adiabatic shear. (3) The difference of UEVC paths will affect the removal mode of materials and form different surface morphology. (4) For different cutting paths, compressive stress is distributed at the lowest point of the machining pit, and tensile stress is distributed at the protrusion position.

High-speed machining of γ-TiAl alloy is a significant challenge due to high cutting temperatures. From the perspective of environmental protection and improving tool life, appropriate cooling strategies should be adopted. Compared with dry and conventional flood cooling conditions, the feasibility of machining γ-TiAl in cryogenic LN₂ cooling conditions was discussed. The cutting force, tool wear and its mechanism, and surface roughness, as well as sub-surface morphology characteristics, were studied by combining macro and micro techniques. The results revealed that the wear morphology of the rake and flank face under the three cooling media shows different degrees. The crater wear of the rake face is expanded at high speeds and then progresses into more serve flaking and notching wear. The main wear pattern on the flank face is gradually transformed from adhesive wear to diffusion and oxidation wear at high speeds in dry machining. In the LN₂ condition, the diffusion of workpiece elements and cutting-edge oxidation were restrained. The wear pattern is still mainly adhesive wear. In addition, cryogenic machining shows significant advantages in reducing cutting force, suppressing heat-affected zone, improving surface quality, and inhibiting micro-lamellar deformation.