The burgeoning market for heavy-cargo transportation poses an increasing challenge to the normal use of highway bridges. This study investigates the vehicle-bridge coupled dynamic response of a twin-tower three-span cable-stayed bridge under the load of heavy-cargo transportation by employing the holistic solution method and the direct integration method. The influence of vehicle load and speed on the dynamic response of the bridge when heavy-cargo transportation vehicles pass through cable-stayed bridges is discussed. The main research conclusions are: (1) The peak stress of the stay cables increases linearly with the increase in load weight. There is a nonlinear relationship between the vibration amplitude of the stay cables and the vehicle load parameters, with the rate of increase in the vibration amplitude accelerating as the load weight increases. (2) The maximum displacement values of the towers show a trend of linear increase with the load parameters. The deflection at the mid-span cross-section increases linearly with the load weight, with an increase of approximately 26.8 mm in mid-span deflection for every additional 100t of load weight. (3) The vehicle speed has a significant influence on the cable vibration amplitude, with the growth rate of the vibration amplitude continuously increasing as the vehicle speed increases. (4) The displacement of two bridge towers shows a positive correlation with vehicle speed variation. The oscillation amplitude of the displacement at the mid-span cross-section shows a clear increase.