The process of machining the modern engineering materials, such as nickel-based superalloys, still requires improvement. This paper focuses on comparing the turning process of Inconel 625 superalloy using three types of cutting inserts to obtain the finishing process. The influence of cutting data, such as cutting speed, feed rate, and cutting depth, on the machined surface quality, surface quality were selected. The novelty of the research, described in the article, is the optimization of the machining of Inconel 625 by using the stepwise selection of parameters. The most important issue is that the stepwise method can be used in industry, where increasingly new nickel-chromium materials with more specific strength properties are used for parts.