With the rapid development of photoelectric communication and other fields, the demand for high-precision aspheric mirrors has been increasing. Predicting dynamic cutting forces is vital in selecting machining parameters and also affects the surface quality of the machined surface. This study comprehensively considers the effects of different cutting parameters and workpiece shape parameters on dynamic cutting force. The actual width of cut, depth of cut, and shear angle are modelled while considering the effects of vibration. A dynamic cutting-force model considering the aforementioned factors is then established. Using experimental results, the model accurately predicts the average value of dynamic cutting force under different parameters and the range of fluctuation of dynamic cutting force, with a controlled relative error of about 15%. The influence of workpiece shape and workpiece radial size on dynamic cutting force is also considered. The experimental results show that the greater the surface slope, the more dramatic the dynamic cutting force fluctuations. This lays the foundation for subsequent writing on vibration suppression interpolation algorithms. The influence of the radius of the tool tip on dynamic cutting forces leads to the conclusion that to achieve the goal of reducing the fluctuation of cutting forces, diamond tools with different parameters should be selected for different feed rates. Finally, a new interpolation-point planning algorithm is used to optimize the position of interpolation points in the machining process. This proves the reliability and practicability of the optimization algorithm. The results of this study are of great significance to the processing of high-reflectivity spherical/aspheric surfaces.