Although numerous studies have tried to explain the mechanism of directional hydraulic fracturing in a coal seam, few of them have been conducted on gas migration stimulated by directional hydraulic fracturing during coal mine methane extraction. In this study, a fully coupled multi-scale model to stimulate gas extraction from a coal seam stimulated by directional hydraulic fracturing was developed and calculated by a finite element approach. The model considers gas flow and heat transfer within the hydraulic fractures, the coal matrix, and cleat system, and it accounts for coal deformation. The model was verified using gas amount data from the NO.8 coal seam at Fengchun mine, Chongqing, Southwest China. Model simulation results show that slots and hydraulic fracture can expand the area of gas pressure drop and decrease the time needed to complete the extraction. The evolution of hydraulic fracture apertures and permeability in coal seams is greatly influenced by the effective stress and coal matrix deformation. A series of sensitivity analyses were performed to investigate the impacts of key factors on gas extraction time of completion. The study shows that hydraulic fracture aperture and the cleat permeability of coal seams play crucial roles in gas extraction from a coal seam stimulated by directional hydraulic fracturing. In addition, the reasonable arrangement of directional boreholes could improve the gas extraction efficiency. A large coal seam dip angle and high temperature help to enhance coal mine methane extraction from the coal seam.