A ballast bed provides a stable foundation and a sufficient vibration-damping performance for a railway line due to its loose and porous structure. Tamping operations change the compactness of ballast stacks and improve and maintain the state of ballast beds, which also affect the vibration-transfer characteristics and resistance performance of ballast beds. In the present study, impact excitation technology was used to test and analyze the influence of the number of tamping operations performed by a tamping car on the damping and stiffness of a ballast bed. Additionally, the influence of different tamping operations on the longitudinal vibration-transmission characteristics of the ballast bed was obtained by the methods of “single-point excitation and multi-point pick-up”. The mode of analysis of the railway structure was carried out by numerical simulation, and the resistance test on site was used to study the evolution law of the longitudinal and lateral resistance of the ballast bed during three tamping operations. The results showed that a large machine tamping operation changed the values of the two dominant resonances (140.75 Hz to 202.35 Hz and 381.25 Hz to 418.75 Hz) of track structure in the range of 0–600 Hz. The tamping operation also affected the resistance, damping, and stiffness of the ballast bed (the longitudinal and lateral resistances decreased by 17.39% and 20.34%, respectively, and the damping and stiffness increased by 204.07% and 148.80%, respectively), which suggests that the longitudinal/lateral resistances, damping, and stiffness of the ballast bed were strongly negatively correlated with one another. The modal shapes of the track structure caused by the first tamping and the second tamping were obviously different, and the positions and values of the maximum displacement changed (1.92 mm to 1.71 mm). The tamping also affected the longitudinal vibration transmission between the sleepers, and the maximum attenuation rate between adjacent sleepers was 81.25%. The change of the resistance work of the ballast bed with the displacement was more significant than the change of the resistance of the ballast bed with the displacement (when the ballast bed resistance decrement rates were 4.34%, 16.19%, and 20.34%, the track bed resistance work decrement rates were 13.14%, 28.15%, and 39.35%, respectively). Thus, the resistance work was more applicable when describing the variational degree of the stability of the ballast bed.