Axial piston pumps are widely used to supply the fluid power, but their significant vibration has become a growing concern. To address this issue, this paper presents a novel dynamic model for the axial piston pump and mitigates both flow fluctuation and mechanical vibration powers through a multi-objective optimization method. A Lumped-Parameter (LP) model is first introduced to describe dynamic behaviors of the entire pump assembly, and the Newmark-β method is adopted to calculate flow fluctuation and mechanical vibration powers. Experimental validation is conducted to ensure the accuracy of the proposed model. Using this validated model, a multi-objective optimization algorithm is employed to optimize the structural parameters of three representative valve plate types, aiming to simultaneously reduce flow fluctuation and mechanical vibrations. The optimization results demonstrate a significant reduction in the pump vibration power, as well as improvements in cavitation and pressure overshoot conditions. Among these optimized designs, the valve plate with hole-shaped damping grooves shows the lowest vibration power, while the valve plate with the triangular damping grooves achieves the lowest maximum piston chamber pressure. This study offers a promising approach for designing quieter axial piston pumps, which promotes the fluid power technology.