This study investigated the mechanisms influencing hydraulic fracture propagation under the influence of cleat complex geometries. The study established a 3D-DEM (three-dimensional discrete element method) model for complex fracture propagation, utilizing the discrete element method and incorporating complex cleat geometries. The model simulates the propagation patterns of hydraulic fractures within coal seams. The findings indicate the following: (1) The fracture width within coal seam cleats undergoes significant variations. A quantification method for these variations and a novel concept of cleat-induced fracture deflection angle are proposed. As the cleat angle increases from 0° to 45°, the cleat-induced fracture deflection angle also increases, reaching 17.1°, demonstrating that cleats have a directional inducing effect on hydraulic fracture propagation; (2) injection hole pressure decreases during fracture capture by coal cleats, whereas pressure escalation occurs during penetration through these cleats; (3) a smaller angle between the face cleat orientation and the direction of maximum principal stress results in longer fracture lengths and narrower fracture widths; and (4) higher injection rates augment the fracture width, facilitating the entry of proppants.