The research presents an analysis and comparison of the Taguchi Design and Response Surface Methodology (RSM) in optimizing the laser cutting machine parameters on dimension accuracy for stainless steel products. The paper studies effects of input factors such as cutting speed, nitrogen pressure, power, and frequency on the quality cutting of stainless steel (304) specimens. In this paper, two objectives are examined: targeting laser-cut edge to perpendicular 90 degrees and maximizing the cutting accuracy. The paper proposes a simple formula to optimize both targets by minimizing one new function definition, i.e., dimensional error. An L9 orthogonal array of Taguchi Methodology is adopted to minimize the number of experiments and shorten analysis time to achieve the optimal parameters. These results are compared with RSM. Box–Behnken Design (BBD) type of RSM requires more experiments than the Taguchi approach. RSM regression models as the quadratic functions of the control factors are developed to minimize the dimensional error of cutting products. Then, Analysis of Variance (ANOVA) and graphs will be analyzed to determine the influences of variables on the responses. Both Taguchi’s method and RSM found that the most influential factor on dimension accuracy is cutting speed, followed by laser power. While Taguchi provides good graphic visualization for quickly predicting the optimum condition, it cannot examine the interaction effects as RSM due to the lack of data. Besides, RSM reveals the percentage contribution of factors on dimensional error. Cutting speed has a maximum contribution, i.e., 39% of the total. The interaction of cutting speed and power contributes 16% of the total. In this study, RSM can predict optimum conditions more accurately than Taguchi. There are misleading results from the Taguchi method compared with RSM. However, the difference between these objective values is insignificant. The validation experiments show that the Taguchi method can be a practical approach for optimization problems. It can help reduce cost and time and achieve the desired optimal outputs. With cutting problems requiring high precision, the RSM method is highly recommended for identifying optimal parameter settings and interaction effects. With problems that their experimental runs consume high cost and time, Taguchi can be a suitable method for screening the significant variables. Although Taguchi and RSM are used widely for optimization problems in many fields, choosing the right methodology for various objectives is still a concern with different arguments and needs further research. Therefore, this study could be an adequate reference for parameter optimization problems in various fields.