Abstract: Gas is a gas generated during the geological evolution of coal, with methane（CH₄） as its main component, often containing carbon dioxide（CO₂） as well. To achieve the goal of carbon neutrality and carbon peak emissions in the coal industry, the strategy of injecting CO₂ into goaf areas to displace CH₄ has been proven effective. This paper takes the Daliuta 5-2 coal seam, Tangjiahui 6 coal seam, and Wenjiazhuang 15 coal seam as engineering cases, utilizing the UDEC discrete element numerical simulation software to delve deeply into the failure and deformation characteristics of coal and rock strata under different mining conditions. Combined with COMSOL finite element numerical simulation technology, a comparative analysis is conducted on the effect of CO₂ displacing CH₄ in two injection methods under various mining conditions. The research results indicate that as the mining height of the coal seam increases, the development of fissures in the coal and rock strata becomes more significant, exhibiting characteristics of advanced development. The stress distribution in the middle of the goaf area is relatively uniform, while stress concentration occurs at both ends. During the mining process, the roof of the coal seam experiences compressive deformation, while the middle of the floor expands, and the two sides are compressed. Further observation reveals that when injection holes are arranged in the middle of the coal seam, the CH₄ gas pressure significantly decreases from 0.74 MPa to 0-6 kPa; whereas when injection holes are placed on both sides, the pressure drops to 0-16 Pa. This demonstrates that CO₂ can effectively displace CH₄, and the arrangement of injection holes on both sides exhibits superior displacement efficiency. Therefore, optimizing the placement of injection holes is crucial for improving the efficiency of CO₂ displacing CH₄. The research findings provide important references for the efficient management of gas in similar mines.