This study addresses the challenges of structural safety and vibration control for intelligent sampling robots operating under extreme and complex road conditions. The aim is to enhance the stability and reliability of heavy-duty mobile platforms subjected to impact and random excitations. Finite element numerical simulations were used to develop models for the platform frame and the complete platform. Static and dynamic response analyses were conducted under combined impact obstacle-crossing and random road spectrum conditions. A multi-index vibration evaluation system was established, followed by the optimization of vibration damping parameters. Subsequently, a lightweight design for a PFRP-steel hybrid structural platform was proposed and validated. The results show that under typical static loading conditions, the maximum von Mises stress and maximum deformation of the platform frame are 68.26 MPa and 0.080 mm, respectively, indicating sufficient strength and stiffness margins. Under obstacle-impact and random road-profile excitations, the vibration responses of the platform are dominated by pitching and rolling modes, respectively, while maintaining favorable attitude stability. The influence of vehicle speed on the vibration level is generally greater than that of the road-profile grade. When the damper damping ratio increases from 0.2 to 0.4, the 5–50 Hz band-limited acceleration peaks under the two random vibration conditions decrease by 35% and 31%, respectively. On this basis, a moderate increase in damper stiffness can further reduce the platform vibration response. Under the premise of satisfying the static stiffness and load-bearing requirements, the proposed PFRP–steel hybrid platform reduces the unloaded mass by approximately 50% and the fully loaded mass by approximately 33%. It can significantly reduce the displacement peak under impact conditions and simultaneously decrease vibration response indicators such as band-limited acceleration RMS and velocity RMS under different operating conditions.