Slow tool servo diamond turning has widespread application in fabricating freeform optics. Previous studies are focused on the methods of the tool path generation and verification of zero-rake-angle tools. However, these methods are unsuitable for non-zero-rake tools that are used for machining hard-and-brittle materials. This paper presents a universal location-point-drive tool path generation method, which caters to arbitrary rake angle tools and the steady X movement feature, and the corresponding universal tool interference check method. Systematic analysis and ultra-precision machining experiments confirmed the feasibility of our methods and present better surface quality and form accuracy compared to the traditional method.