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We present a source catalog from the first deep hard X-ray ($E>10$ keV)survey of the Small Magellanic Cloud (SMC), the NuSTAR Legacy Survey of theSMC. We observed three fields, for a total exposure time of 1 Ms, along the barof this nearby star-forming galaxy. Fields were chosen for their young stellarand accreting binary populations. We detected 10 sources above a 3$\sigma$significance level (4$-$25 keV) and obtained upper limits on an additional 40sources. We reached a 3$\sigma$ limiting luminosity in the 4$-$25 keV band of$\sim$ $10^{35}$ erg s$^{-1}$, allowing us to probe fainter X-ray binary (XRB)populations than has been possible with other extragalactic NuSTAR surveys. Weused hard X-ray colors and luminosities to constrain the compact-object type,exploiting the spectral differences between accreting black holes and neutronstars at $E>10$ keV. Several of our sources demonstrate variability consistentwith previously observed behavior. We confirmed pulsations for seven pulsars inour 3$\sigma$ sample. We present the first detection of pulsations from aBe-XRB, SXP305 (CXO J005215.4$-$73191), with an X-ray pulse period of$305.69\pm0.16$ seconds and a likely orbital period of $\sim$1160-1180 days.Bright sources ($\gtrsim 5\times 10^{36}$ erg s$^{-1}$) in our sample havecompact-object classifications consistent with their previously reported typesin the literature. Lower luminosity sources ($\lesssim 5\times 10^{36}$ ergs$^{-1}$) have X-ray colors and luminosities consistent with multipleclassifications. We raise questions about possible spectral differences at lowluminosity between SMC pulsars and the Galactic pulsars used to create thediagnostic diagrams.

Neutron Stars and Black Holes in the Small Magellanic Cloud: The SMC NuSTAR Legacy Survey