The earth's topography is generally rough at various scales. Numerical simulation techniques are used in this study to investigate the energy attenuation of regional phases across a randomly rough topography. We demonstrate a clear statistical correlation of the distance-dependent energy distribution with path topographic properties parameterized by the surface correlation length a and the surface root-mean-square height σ. Numerical experiments show that interference of randomly scattered waves by topography can cause regional wave amplitude undergoing strong variations. The topographic-scattering-driven energy distribution over a long distance is usually characteristic of an attenuation trend on the long distance scale, accompanied by amplitude fluctuations on the smaller distance scale. Total energy attenuation can be divided into large-scale and small-scale components that are correlated, respectively, in quite different manners, with along-path topographic statistics. On the one hand, the small-scale energy component is strongly related to the near-receiver topographic geometry. It has a striking similarity to the corresponding topographic curve. The spatial fluctuation of the small-scale component depends on a, whereas its amplitude amplification/deamplification is mainly related to σ, wavelength, and local incident angles. On the other hand, the large-scale component of energy curve, described by a scattering Q, demonstrates a scale-dependent relation with topographic statistics. A two-step analysis method is presented to evaluate the mantle leakage loss due to topographic scattering. The resultant topographic scattering Q is comparable with some observations with Q measured as a mean value in the crust. In summary, the study suggests the concept that topographic scattering might be a powerful mechanism to attenuate regional waves.