To investigate the optimal longitudinal seismic energy dissipation system of straddle-type monorail-cum-road long-span cable-stayed bridges, the Niutianyang Bridge was selected as the engineering background, and the explicit time-domain dimension-reduced iteration method was adopted to carry out nonlinear time-history analysis. To consider the dynamic characteristics of longitudinal movable supports, the static and dynamic responses of four kinds of energy dissipation systems were studied, including longitudinal unconstrained, elastic cable, viscous damper, and speed lock-up devices. The damping effect of four types of schemes in which viscous dampers were installed at piers or towers was analysed, and the parameters of the viscous dampers were optimised. The influences of the straddle-type monorail train braking force and the running vibration of the straddle-type monorail traffic on the parameters of the viscous dampers were analysed. This study shows that the viscous damper system had the lowest bending moment at the bottom of the tower and a smaller displacement response, and the energy dissipation was the best. Each viscous damper had the highest energy dissipation efficiency when they are installed only at the main tower. The damping effect was better when the damping coefficient c ranged from 3500 to 5000 kN⋅m/s−α and the velocity exponent α ranged from 0.35 to 0.5. The static friction of the straddle-type monorail-cum-road long-span cable-stayed bridge support can resist the trains’ braking force, and the parameters of the viscous damper can be selected regardless of train braking. A suitably large value of velocity exponent α may be required to increase the working velocity of the viscous damper to reduce the damper’s participation in the process of the train crossing the bridge.