The objective of this study is to explore the impact of process parameters on the cut width and heat affected zone (HAZ) width of micro-channels manufactured using fiber laser on copper work piece. The study aimed to identify the optimal values for these responses. The analysis was conducted using response surface methodology (RSM), where tests were performed according to a predetermined experimental design. The scanning speed, pulse frequency, and working power were varied during the trials. The present study aims to elucidate and examine the operational principles underlying the creation of micro-channels on pure copper using a fiber laser operating at a wavelength of 1064 nm. Ultimately, by identifying the most effective combination of process parameters, the best values for both the width of the cut and the width of the heat affected zone (HAZ) are attained. This research study offers a comprehensive technical framework for the application of fiber laser processing on pure copper.