Superalloys, commonly referred to as high-performance alloys, possess remarkable characteristics that enable them to operate effectively at temperatures significantly surpassing their melting points. These alloys exhibit exceptional strength properties (i.e., corrosion resistance, high tensile strength, creep resistance, rupture strength, and the ability to retain their strength even at elevated temperatures). These inherent properties of superalloys introduce intricate challenges during the machining or cutting process, resulting in unforeseen and abrupt modifications to the interaction between the workpiece and the cutting tool. The fluctuations in interactions can give rise to inconsistencies in the surface finish of the work material. This research focuses on the characterization/classification of variations in surface roughness during face milling of INCONEL 625 using cutting force signals. Additionally, the study investigates the influence of machining parameters on cutting forces and surface roughness. The research considers five levels for each cutting parameter, including feed rate, cutting speed, and depth of cut. Interaction plots are generated to analyze the relationship between machining parameters and responses, namely surface roughness and cutting forces. In order to classify the surface roughness, a proposed methodology is employed, aiming to identify different classes such as refined, good, and satisfactory surface finishes during milling. Both time domain and frequency domain characteristics of the cutting force data collected during milling are utilized to determine surface quality. Bayesian optimized Support Vector Machine (SVM) and Artificial Neural Network (ANN) models are employed, and a comparison is conducted between them. The SVM model achieved an accuracy of 99.61%, while the ANN model slightly outperformed with an accuracy of 99.74%.