We present the results of two-dimensional radiation-hydrodynamic simulations of expanding supernova ejecta with a central energy source. As suggested in previous multi-dimensional hydrodynamic simulations, a sufficiently powerful central energy source can blow away the expanding supernova ejecta, leading to efficient mixing of stratified layers in the ejecta. We assume that the energy injection is realized in the form of non-thermal radiation from the wind nebula embedded at the center of the ejecta. We found that the multi-dimensional mixing in the ejecta assists the injected non-thermal radiation escaping from the ejecta. When the non-thermal radiation is absorbed by the ejecta, it is converted into bright thermal radiation or is consumed as the kinetic energy of the supernova ejecta. We found that central energy sources with the injection timescale similar to the photon diffusion timescale realize an efficient conversion of the injected energy into thermal radiation. On the other hand, a rapid energy injection ends up accelerating the ejecta rather than giving rise to bright thermal emission. This remarkable difference potentially explains the diversity of energetic supernovae including broad-lined Ic and superluminous supernovae.