Steel truss–arch composite bridge systems are widely used in bridge engineering to provide sufficient space for double lanes. However, a lack of research exists on their mechanical performance throughout their lifespan, resulting in uncertainties regarding bearing capacity and the risk of bridge failure. This paper conducts a numerical study of the structural mechanical performance of a flexible arch composite bridge with steel truss beams throughout its lifespan to determine the critical components and their mechanical behavior. Critical vehicle loads are used to assess the bridge’s mechanical performance. The results show that the mechanical performance of the bridge changes significantly when the temporary piers and the bridge deck pavement are removed, substantially influencing the effects of the vehicle loads on the service life. The compressive axial force of the diagonal bar significantly increases to 33,101 kN near the supports during the two construction stages, and the axial force in the upper chord of the midspan increases by 4.1 times under a critical load. Moreover, the suspender tensions and maximum vertical displacement are probably larger than the limit of this bridge system in the service stage, and this is caused by the insufficient longitudinal bending stiffness of truss beams. Therefore, monitoring and inspection of critical members are necessary during the removal of temporary piers and bridge deck paving, and an appropriate design in steel truss beams is required to improve the life cycle assessment of this bridge system.