Burrs prevent the proper assembly of components. Consequently, industrial manufacturers resort to secondary operations for burr removal, which increases both production time and costs. Multiple factors contribute to burr formation, among which tool wear is a primary cause in drilled parts. Micro- and nano-texturing of cutting tools represents a novel approach to mitigating hole burring and tool wear. In this study, micro-grooves with widths ranging from 200 to 400 μm, inter-groove spacings of 200 to 400 μm, and orientation angles of 0° to 90° relative to the cutting edge were fabricated on the flank face of a drill bit, and the impact of micro-groove geometry on tool wear and hole burr formation was investigated. Furthermore, the optimization of micro-groove geometric parameters to minimize both wear and burr formation—conducted both individually and through a multi-objective approach considering these two output parameters simultaneously—has been performed using the response surface method (RSM). Statistical analysis indicates that increasing the micro-groove width and inter-groove spacing from 200 to 400 μm reduces tool wear. Additionally, as the micro-groove orientation angle increases from 0° to 90°, tool wear initially increases and subsequently decreases. Increasing the inter-groove spacing from 200 to 400 μm and increasing the orientation angle relative to the cutting edge from 0° to 90° leads to an increase in burr width.