The development of methane (CH4)/dimethyl ether (DME) combustion systems can reduce fossil energy consumption and pollutant emissions of gas turbines while enhancing fuel diversity. However, employing detailed kinetic mechanisms in the fluid dynamics calculations for the design and optimization of CH4/DME burner configurations is enormously costly for computational resources and time. Therefore, reduced kinetic mechanisms are essential for widespread implementation. In the current work, 1200 + iterations based on the genetic algorithm were performed with 30 target conditions, which extracted a reduced mechanism from the detailed CH4/DME chemical kinetic mechanism. It contained 35 species and 131 reaction steps that reasonably captured the detailed mechanism's main reaction path. Measurements from a shock tube verified that the reduced mechanism provides reasonable predictions of ignition delay times for pure methane, pure DME, and CH4/DME mixtures at T > 1300 K, 1050 K, and 1100 K, respectively. The addition of CH3O2 reaction schemes and modification CH3OCH2 related reactions extended the temperature range to T > 900 K, 700 K, and 760 K under stoichiometric and fuel-rich conditions. The accuracy of the reduced and optimized mechanism was also confirmed by other results obtained from laminar flames, counter-flow diffusion flames, and flow reactors. Accurate replication of the temperature and species profiles was achieved for the numerical simulation of the turbulent flames by the optimization mechanism, which also decreased nearly half the computational time compared to the detailed mechanism. Overall, there is a suitable balance between accuracy and computational efficiency, as shown by the reduced mechanism, promising potential computational cost savings for large-scale numerical combustion simulations.