Deep coal seams are characterized by large stress, high gas pressure, and low permeability. The gas disaster threatens the safe production of coal mine seriously. Gas extraction by crossing-seam boreholes from floor roadway (GECMBFR) can reduce the pressure and content of coal seam gas, which is the main measure to prevent gas disaster. Considering the Klinkenberg effect, governing equations of gas adsorption/desorption-diffusion, gas seepage, and stress fields within the coal seam are established to form the seepage-stress coupling model. The governing equations are embodied into a finite element driven software to numerically simulate gas migration and fluid-solid coupling law in coal seam. On this basis, the process of gas extraction under different borehole spacings and diameters is simulated. The effects of these two key parameters on coal seam gas pressure, gas content, and gas permeability were analyzed. The borehole spacing and diameter were determined to be 5 m and 0.09 m, respectively. Combined with the actual situation of a mine, the process of gas extraction from floor roadway with different cross-sectional schemes, ordinary drilling boreholes and punching combined drilling boreholes, is comparatively analyzed. The results show that the gas extraction effect by ordinary drilling boreholes is lower than that of the punching combined drilling boreholes, and the extraction is uneven and makes it difficult to meet the standard. Hydraulic punching was carried out, and coal was washed out of the borehole, which expanded the contact area between the borehole wall and coal seam. The coal seam around the punching borehole is unloaded, which improves coal permeability and accelerates gas migration towards the borehole, thus promoting the efficiency of gas extraction. It is more reasonable to use punching combined drilling borehole scheme when implementing the GECMBFR technology.