Milling is the surface machining process by removing material from the raw stock using revolving cutters. This process accounts for a major stake in most of the Original Equipment Manufacturing (OEM) industries. This paper discusses optimizing process parameters for machining the AA 2014 T 651 using a vertical milling machine with coated cutting tools. The process parameters such as cutting speed, depth of cut, and type of the cutting tool with all its levels are identified from the previous literature study and several trial experiments. The Taguchi L9 Orthogonal Array (OA) is used for the experimental order with the chosen input parameters. The commonly used cutting tools in the machining industry, such as High-Speed Steel (HSS) and its coated tools, are considered in this study. These tools are coated with Titanium Nitride (TiN) and Titanium Aluminum Nitride (TiAlN) by Physical Vapor Deposition (PVD) technique. The output responses such as cutting forces along the three-axis are measured using a milling tool dynamometer for the corresponding input factors. The input process parameters are optimized by considering the output responses such as MRR, machining torque, and thrust force. Grey Taguchi-based Response Surface Methodology (GTRSM) is used for multiobjective multiresponse optimization problems to find the optimum input process parameter combination for the desired response. Polynomial regression equations are generated to understand the mathematical relation between the input factor and output responses as well as Grey Relational Grade (GRG) values. The optimum process parameter combination from the desirability analysis is the HSS tool coated with TiAlN at a cutting speed of 270 rpm and a depth of cut value of 0.2 mm.