In this work, fiber laser trepan drilling is conducted on a thin sheet of titanium grade 2 alloy. The parametric impact of average laser power and trepanning speed on response characteristics like material removal rate (MRR), overcut at the top, and overcut at the bottom is studied after conducting a full factorial of nine experimental sets. Analysis of variance (ANOVA) was implemented to study the percentage contribution and significance of each process variable on the performance characteristics. According to ANOVA results, average laser power is the most significant process variable for all performance characteristics. In addition, “multi-objective optimization on the basis of ratio analysis (MOORA)” is used to optimize all of the response measures simultaneously. The optimal condition recommended by MOORA with the greatest assessment value is an average power: 25 watts and a scanning speed: 30 mm/s.