Path planning and tracking serve as the foundational elements for the navigation of deep-sea mining vehicle (DSMVs) and are indispensable to the safety and productivity of mining endeavors. This paper proposes a novel method, named QuatAPF, for DSMVs to facilitate safe and energy-efficient motion under intricate underwater environment. The proposed QuatAPF method is primarily composed of two stages, i.e., path planning and path tracking. During the path planning phase, four specialized artificial potential fields are crafted to compute the optimal navigation path points, which ensures the safety, efficiency, and energy conservation of DSMVs during mining operations. Then, in the path tracking phase, the model predictive control (MPC) is employed to enable precise navigation and ensure accurate tracking of the planned path. To validate the proposed method, a dedicated simulation test platform was constructed, where the method was rigorously evaluated across a range of diverse scenarios. Results illustrates that, the incorporation of repulsive potential field and vortex field ensures collision-free navigation during mining operations in the presence of both static and dynamic obstacles. The construction of midline gravitational potential field minimizes deviation from the designated midline, improving the mining efficiency by at most 9.24% compared with two test methods. The inclusion of deep-sea ocean current potential field facilitates energy-efficient motion by strategically leveraging the natural forces of deep-sea currents, which reduces the energy consumption by up to 15.81% and 14.01%, respectively.