A supra-massive neutron star (NS) spinning extremely rapidly could survive from a merger of NS-NS binary. The spin-down of this remnant NS that is highly magnetized would power the isotropic merger ejecta to produce a bright mergernova emission in ultraviolet/optical bands. Before the mergernova, the early interaction between the NS wind and the ejecta can drive a forward shock propagating outwards into the ejecta. As a result, a remarkable amount of heat can be accumulated behind the shock front and the final escaping of this heat can produce a shock breakout emission. We describe the dynamics and thermal emission of this shock with a semi-analytical model. It is found that sharp and luminous breakout emission appears mainly in soft X-rays with a luminosity of \(\sim10^{45}~\rm erg~s^{-1}\) at a few hours after the merger, by leading the mergernova emission as a precursor. Therefore, detection of such an X-ray precursor would provide a smoking-gun evidence for identifying NS-powered mergernovae and distinguishing them from the radioactive-powered ones (i.e., kilonovae or macronovae). The discovery of NS-powered mergernovae would finally help to confirm the gravitational wave signals due to the mergers and the existence of supra-massive NSs.