The surfaces with textures have been widely used as functional surfaces, and the textures are usually generated on flat or cylindrical surfaces. Textured freeform surfaces will have more potential applications. The authors have proposed the double-frequency elliptical vibration cutting (DFEVC) method to machine freeform surfaces on steel materials. Based on this method, a new diamond turning method is developed, in which the variable-frequency modulations are utilized to control the tool marks left on the machined surface to generate the micro/nano dimple textures with high uniformity on the freeform surface. Different from the conventional surface topography model based on the ideal tool cutting edge with zero cutting edge radius, a new modeling approach based on the tool surface profiles is proposed, in which the rake face, the flank face, and the cutting edge surface with actual non-zero cutting edge radius instead of the ideal cutting edge are included for the tool model, the tool surfaces during the machining process are analytically described as a function of the tool geometry and the machining parameters, and the influences of the tool surface profiles on the topography generation of the machined surface are considered. A typical freeform surface is textured on die steel, and the measured results verify the feasibility of the proposed turning method. Compared with the topography prediction results based on the ideal cutting edge, the results considering the tool surfaces show improved simulation accuracy, and are consistent with the experimental results, which validates the proposed topography prediction approach.