  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.
