To reduce the adverse impact of demolition of the symmetrical rigid frame arch bridge overcrossing the highway with over-saturated traffic flow, a rapid demolition method based on the Self-Propelled Modular Transporter (SPMT) technique was developed in this study. The calculation formulae for reaction forces of the supporting brackets, as well as driving force and stability of SPMTs, were derived by analyzing the stability, synchronization, and influencing parameters of the cut bridge body—transport system. In addition, a monitoring system during the whole process was developed to ensure the demolition safety. An application of demolishing a crossline symmetrical rigid frame arch bridge in China within 5 h has been presented. The results showed that the proposed method can be successfully applied in real projects, leading to significant reduction in traffic impact, energy consumption, and environmental pollution.