The two-dimensional (2D) piston pump utilizes a cam guide-roller two-degree-of-freedom (2DOF) motion mechanism, making it adaptable to a wide range of variable operating conditions and frequent loaded startups in the context of motor-driven systems. Volumetric efficiency, which measures the ratio of actual to theoretical output flow, is vital for optimizing hydraulic pump performance and reducing energy loss. This study established a mathematical model for the 2D piston pump, considering factors like axial internal and external leakage, circumferential leakage, backflow, fluid compressibility, turbulence, and flow coefficients. The model was built using a co-simulation environment integrating AMESim and Simulink. Simulation results showed that volumetric efficiency increases with higher rotational speeds and decreases with higher pressures. High-pressure backflow is a key factor in adversely affecting volumetric efficiency and requires special attention. Experimental validation was conducted across a speed range of 500--3000 r/min and pressure range of 1--28 MPa. The lowest efficiency recorded was 64.81% at 500 r/min and 28 MPa, with a maximum deviation of 3.28% from the simulation. At 3000 r/min and 28 MPa, the efficiency was 89.53%, deviating by 1.69% from the simulation. The close correspondence between experimental and simulation results validates the model's reliability in predicting volumetric efficiency.