The laser micro-cutting process is the most widely applied machining process, which can be applied to practically all metallic and non-metallic materials. While this had challenges in cutting quality criteria such as geometrical precision, surface quality, and numerous others. This article investigates the laser micro-cutting of PEEK composite material using nano-fiber laser due to the significant importance and efficiency of laser in various manufacturing processes. Design of Experiential tool based on Response Surface Methodology (DoE-RSM) Central Composite Design (CCD) used to generate the statistical model. This method was employed to analyze the influence of parameters, including laser speed, laser power, laser frequency, and the number of passes on the cutting characteristics-and geometrical. Cuttinggeometry requirements are significant quality features since they are one of the metrics for the geometrical precision of micro-cutting process. It was concluded that higher laser power, slower speed, and more pass number result in a low kerf taper; these parameters significantly impact the other cutting characteristics and groove geometry. Whereas the frequency has a lower impact on the cutting geometry. Finally, the experiments show that the maximum cutting depth was 2000𝜇m, with minimum upper width of 305.56 µm and a minimum angle of 2.8906o.