To investigate the influence of laser cutting processing parameters on the cutting quality of 304 stainless steel with a thickness of 1 mm, a Box-Behnken experiment was designed. A 2 kW fiber laser cutting machine was employed to perform this process while a 3D measurement microscope and precision electronic scale were utilized to gauge the sectional roughness and slag thickness respectively. The study sought to analyze how different process parameters (namely: laser power, cutting speed, auxiliary gas pressure, defocusing amount) influenced the cutting quality. The experimental results show that both laser power and cutting speed significantly impacted the slag thickness, whereas laser power and defocusing amount considerably affected roughness. Drawing upon these experimental results, the response surface method was adopted to develop a three-dimensional response surface model representing both surface roughness and slag thickness. According to the fitting results of the response surface model, and taking the minimum slag thickness and roughness as the index, the laser cutting process parameters were optimized using a genetic algorithm. This yielded a set of optimal process parameters: laser power at 1,175 W, cutting speed at 3.55 m/min, auxiliary gas pressure at 1.55 MPa, and defocusing amount at 0.48 mm.