Power skiving is a promising method that can enhance the efficiency of gear machining. The machining mechanism is complicated due to several factors, such as the continuous variation in the rake angle and undeformed chip thickness. The tool wear process is also difficult to be evaluated due to the constantly varying in cutting conditions. Hence, to make a comprehensive understanding of the cutting process, we proposed a parametric modeling process based on the kinematics of power skiving. In this model, the undeformed cutting chip was calculated in each pass and shows the consistency with deformed cutting chip in experiments. The effective rake angle and undeformed cutting chip thickness were defined, calculated, and displayed on undeformed cutting chip for a better understanding of the cutting process. The cutting force and tool crater wear were calculated by estimating the distribution of the stress and temperature on the rake face of the cutting tool. Multiple radial-feed experimental evaluations were conducted with the gears of construction vehicles. In the results, the predicted margin of the absolute error of the normal force on the rake face was under 5% in every pass. The wear distribution on the rake face is consistent with the superimposed tool-chip contact area. The results show high potential for the optimization of the cutting tool or cutting conditions in gear power skiving.