Optimizing the influencing parameters of turning operation is a precious thing which determines the desired level of quality in Material Removal Rate (MRR) and Surface Roughness (SR). In this investigation, Taguchi based Grey Relational Analysis (GRA) has been used optimizing the effective process parameters such as depth of cut, feed rate and cutting speed on Stainless Steel 303 (SS 303) material while the specimen is turned with PVD (TiAlN) coated cutting tool. The experimental combinations have been planned based on Taguchi’s Design of Experiments technique. The optimal input parameter combination has been identified as 600 m min−1 spindle speed, 0.1 mm rev−1 feed rate and 0.2 mm depth of cut. The most influencing factor affecting the overall responses of turning process has been found out using Analysis of Variance approach as spindle speed (37.91%). Second-order mathematical models have been developed using Design Expert software for all the considered output responses, which provide the experimental values within the considered range of process parameters even without performing the actual experimentation. 3D surface plots have been generated and analyzed for interpreting the correlation between the process variables. SEM images taken on the machined surfaces and chips have been analyzed and presented in order to validate the optimization results.