Single-point diamond turning (SPDT) is an emerging process for achieving nanometric surface finish, required in various optical devices made from metals like aluminum, copper, and nonmetals like polymers. The optical devices are manufactured in different shapes and profiles, preferably flat and curved surfaces. During the manufacturing of optical devices, controllable and noncontrollable parameters affect the desired surface finish. In this article, controllable machining parameters such as the incremental distance of X slide, feed rate, spindle speed, and depth of cut are selected to study their effect on surface finish and vibration generation of the curved surface. The chosen workpiece material is polymethylmethacrylate (PMMA). Design of experiment (DoE) is used to find out the optimum parameters of surface finish and infeed vibration responses. According to the Taguchi and analysis of Variance (ANOVA) analysis, the feed rate is the most influencing parameter for surface roughness, and incremental distance is for infeed vibration. A confirmation test is carried out to verify the experimental responses with a mathematical regression model, and it shows a close difference within 2.7 percent. Further, minimum surface roughness is perceived as 12.4 nm, corresponding to an infeed vibration amplitude of 4.9 µm/s2, which is signified at a lower frequency.