In order to increase productivity and improve the quality of the machined parts, the metal cutting industries are doing a lot of research work in today’s world. The optimization method in any of the manufacturing processes is considered to be a very vital tool for the continual development of output quality in the product as well as in the process. Therefore, the work is carried out to optimize the process parameters (feed, depth of cut, and cutting speed) of a finished hard turning process for EN 31 tool steel using coated carbide inserts. The EN 31 tool steel is hardened steel and has a wide application in the field of tooling industries. The EN 31 machining process tool steel is typically regarded as challenging due to a number of intrinsic characteristics, including high hardness, high strength, and rapid strain hardening. The goal of the experiment design is to optimize the chosen process parameters using Taguchi’s orthogonal array L9. Grey relational theory is applied for turning EN 31 tool steel in minimum quality lubricant (MQL) condition, an eco-friendly cutting fluid, which is soyabean oil. It is selected in view of the better biodegradability of this fluid so that it can be used in future and can be enhanced in machining operations. The cutting forces and surface roughness are chosen as output response variables. Ultimately, a depth of cut of 0.25 mm, a feed of 0.1 mm/rev, and a cutting speed of 50 m/min represent the multiresponse best parametric combination. The depth of cut and cutting speed are found to be dominating parameters for selected output responses.