As an effective carbon utilization technology, the injection of N2/CO2 mixtures into coal seams has significant potential for improving coalbed methane recovery. Considering the technical barrier that injection of pure CO2 decreases the well injectivity index and pure N2 injection leads to the rapid methane recovery, a method of injecting N2‐enriched gas mixtures with a constant component is proposed. In this study, a thermo‐hydro‐mechanical (THM) coupling numerical model for enhanced coalbed methane (CBM) recovery by injecting N2/CO2 mixtures is established. This model includes complex interactions of coal deformation, competitive adsorption, ternary gas seepage, and heat transfer. The THM coupling model is first validated, and then applied to investigate the evolution of mixed gas concentrations, reservoir permeability, reservoir temperature, CH4 production, and N2/CO2 storage during N2/CO2 enhanced CBM recovery. The results show that the displacement radius and concentration of the mixed gas in the coal seam increased with gas injection pressure increase. The concentration of CH4 gradually decreased with time, and the early decline is faster than the later stage. The sweep of the N2 flow accelerates CH4 desorption and migration, promoting a reduction in reservoir temperature near the production well. Reservoir permeability evolution results from the combined effects of ternary gases (CH4, CO2, N2) competitive adsorption, gas pressure, and geostress on the coal seam within the THM fields. At the methane natural depletion stage (within 250 days), the permeability of coal reservoir first decreases and then increases. With the arrival of the N2/CO2 mixture, the permeability decreases dramatically. From the perspective of cumulative CH4 production, the optimal composition is dominated by the synergistic effect of maximizing breakthrough time and minimizing coal matrix swelling. For 30% CO2‐70% N2, the CH4 recovery ratio reached 71.76%, representing an increase of 16.67% compared to natural depletion.