  Understanding the origin of the flaring activity from the Galactic center
supermassive black hole, Sagittarius A*, is a major scientific goal of the
NuSTAR Galactic plane survey campaign. We report on the data obtained between
July 2012 and April 2015, including 27 observations on Sgr A* with a total
exposure of ~ 1 Ms. We found a total of ten X-ray flares detected in the NuSTAR
observation window, with luminosities in the range of $L_{3-79~keV}$~$(0.2-4.0)
\times 10^{35}~erg~s^{-1}$. With this largest hard X-ray Sgr A* flare dataset
to date, we studied the flare spectral properties. Seven flares are detected
above 5{\sigma} significance, showing a range of photon indices ({\Gamma} ~
2.0-2.8) with typical uncertainties of +/-0.5 (90% confidence level). We found
no significant spectral hardening for brighter flares as indicated by a smaller
sample. The accumulation of all the flare spectra in 1-79 keV can be well fit
with an absorbed power-law model with {\Gamma}=2.2+/-0.1, and does not require
the existence of a spectral break. The lack of variation in X-ray spectral
index with luminosity would point to a single mechanism for the flares and is
consistent with the synchrotron scenario. Lastly, we present the quiescent
state spectrum of Sgr A*, and derived an upper limit on the quiescent
luminosity of Sgr A* above 10 keV to be $L_{Xq, 10-79 keV}$ < $(2.9{\pm}0.2)
\times 10^{34}~erg~s^{-1}$.
