Titanium alloys are widely used in various fields because of their high strength, excellent corrosion resistance, and high heat resistance. As a new advanced titanium alloy for aviation, TC21 titanium alloy has high strength and poor machinability. It is of great significance to study the cutting mechanism of this alloy and the methods to improve the machinability of aircraft. In this paper, aiming at the difficult machinability of titanium alloy TC21, EPH online heating assisted cutting method is put forward for the first time. During the cutting experiment, the TC21 alloy sample was heated to a variety of temperatures through the electric pulse thermal heat technique. Chip shape and cutting force under different heating temperatures were obtained by cutting experiments. In order to study the influence of the heat-assisted cutting process on the machining of TC21 alloy, the orthogonal finite element model was proposed to simulate the heat-assisted cutting process of TC21 alloy. Through this simulation, chip formation, cutting force, and cutting temperature variation were all obtained. The chip formed by the simulation was in accordance with the actual chip. The results demonstrate that the influence of heat-assisted machining on chip morphology of titanium alloy is relatively small, but it has a significant influence on cutting force and surface roughness. The results show that when the sample is heated to 600°C, the surface quality is the best and cutting force can be reduced by more than 40%.