The construction process of steel–concrete composite girders was simulated using a 3D finite-element model and suspension-bracing method. The influences of multiple factors such as self-weight of suspension bracket, wind load, longitudinal spacing of suspension points, concrete deck slab thickness, concrete casting process, and suspension bracket removal on the mechanical properties of the main steel girder and the composite girder were analyzed. The mechanical behavior of the steel–concrete composite girders during the construction process using the suspension-bracing method was revealed. The results show that (1) the normal stress and displacement of the steel girder increases with the increase of the weight of the suspension bracket, and they have a relatively large impact on the increase. (2) The wind load during the construction process will produce large transverse displacement of the main steel girder, the transverse wind load should be considered in the load combination analysis, and necessary measures should be taken to limit the transverse displacement of the main steel girder during the deck casting process. (3) The displacement and stress of the main steel girder will show a parabolic change with the change of the longitudinal spacing of the suspension points, so the optimal value of the longitudinal spacing of the suspension points is recommended to be 4 m. (4) The maximum midspan displacement and stress of the main steel girder increase with the increase of the deck slab thickness, and the weight of the deck slab occupies the main position in the whole system force. (5) In the process of casting deck slabs with the suspension-bracing method, the stress and deformation of the main steel girder increase with the concrete construction stage of the deck slabs. To ensure that the geometric shape of the bridge at each stage is consistent with the theory result, the design elevation of each section should be preraised during the construction process according to the vertical displacement and deformation of the main steel girder caused by the construction of each casting stage. In addition, the upward rebound of the main steel girder caused by the removal of the suspension bracket must be fully considered when setting the prearch of the steel–concrete composite girder.