Hydraulically interconnected suspensions have nonlinear stiffness and damping characteristics, which can provide excellent ride comfort. At the same time, a reasonable suspension connection form can improve the handling performance of a vehicle, and they are widely used in mining vehicles. The working environment of a mining dump truck is harsh, which puts forward higher requirements for the suspension system. In order to study the influence of structural parameters on the performance of hydraulic interconnected suspensions, this paper takes an anti-roll hydraulic interconnected suspension of a tri-axle mining truck as the research object and establishes a mechanical–hydraulic coupling model for the whole vehicle by means of the impedance matrix transfer method and system boundary conditions. The suspension performance evaluation functions are obtained by combining the random pavement input matrix, and the sensitive parameters affecting the suspension performance are found using the Morris analysis method. The results show that the vehicle bounce modal is the most sensitive to changes in the suspension structure parameters, followed by the roll modal, and the pitch modal is the least sensitive. The upper and lower cylinder area ratios, the precharge volume, and the pressure of the front axle accumulator have the greatest influence on the performance of the suspension. The results provide a reference for the optimal design of the hydraulic interconnected suspension of a tri-axle heavy vehicle.