The operational capability of high-speed railways after an earthquake is crucial in post-seismic rescue efforts. In this study, the impact of seismic-induced residual deformations and stiffness degradation on the post-seismic operational capabilities of high-speed railway bridges was explored. A comprehensive post-seismic operational performance analysis of high-speed trains was conducted by integrating seismic-induced residual geometric irregularities of the track surface with dynamic irregularities of the track-bridge system. Further, post-seismic running speed demands for high-speed trains were proposed, and the amplitude limits for seismic-induced track irregularities were defined based on probability assurance rates under varied states of train operational performance indicators. In addition, the impact of ground motion intensity on the running speed demands of high-speed trains, emphasizing safety, was examined, identifying a spectrum of sensitive wavelengths for seismic-induced track irregularities that could influence lateral vibrations of high-speed trains at various speeds. The results indicate that the post-seismic operational capacity of the track-bridge system and the running speed demands for high-speed trains diminish as ground motion intensity increases. Further, the performance indicators for high-speed trains significantly increase with the amplitude of seismic-induced irregularities. Relying on the derailment coefficient as a safety measure tends to overestimate the post-seismic operational capacity of the track-bridge system. The derailment coefficient for high-speed trains significantly increases as the wavelength of post-seismic track surface irregularities decreases. Therefore, mid-range seismic-induced track irregularities, particularly those spanning 30–70 m, warrant increased attention within the 150–350 km/h speed range.