In the faint short gamma-ray burst sGRB 170817A followed by the gravitational waves (GWs) from a merger of two neutron stars (NSs) GW170817, the spectral peak energy is too high to explain only by canonical off-axis emission. We investigate off-axis appearance of an sGRB prompt emission scattered by a cocoon, which is produced through the jet-merger-ejecta interaction, with either sub-relativistic or mildly-relativistic velocities. We show that the observed properties of sGRB 170817A, in particular the high peak energy, can be consistently explained by the Thomson-scattered emission with a typical sGRB jet, together by its canonical off-axis emission, supporting that an NS-NS merger is the origin of sGRBs. The scattering occurs at $lesssim 10^{10}$--$10^{12},{rm cm}$ not far from the central engine, implying the photospheric or internal shock origin of the sGRB prompt emission. The boundary between the jet and cocoon is sharp, which could be probed by future observations of off-axis afterglows. The scattering model predicts a distribution of the spectral peak energy that is similar to the observed one but with a cutoff around $sim$ MeV energy, and its correlations with the luminosity, duration, and time lag from GWs, providing a way to distinguish it from alternative models.
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