Locomotion failure is the challenge for wheeled robots applied in granular media, which puts a high demand on the design of wheels. Due to a lack of a mechanical analysis method that can analyze the dynamic interaction between wheel and granular media, it is a challenge to seek design guidance for the wheel geometry. To this end, we introduce a Dynamic Resistive Force Model (DRFM) method suitable for 3D dynamic intrusion. In this method, Granular Resistive Force Theory (RFT) can be extended to 3D RFT smoothly by using granular parameters, and additional velocity terms can describe the effect of intrusion velocity on intrusion force. The relationship between wheel geometry and mechanical properties can be established by performing differential processing on the wheel surface and integrating the force generated by each micro-surface. On this basis, a complete set of solutions is proposed for the design of mobile robot wheels in granular media, and the screw-propelled wheel is taken as an example to optimize it. Theories, simulations, and experiments have all proved that the optimized wheel can produce greater thrust and lift than normal screw-propelled wheel when ensuring the stability of smooth propulsion. The proposed solution and the optimized screw-propelled wheel bring insights for designing mobile robots in granular media.