The resonant excitation of neutron star (NS) modes by tides is investigated as a source of short gamma-ray burst (sGRB) precursors. I show that the driving of a crust-core interface mode can lead to shattering of the NS crust, liberating ~1046-1047 erg of energy seconds before the merger of a NS-NS or NS-black hole binary. Such properties are consistent with Swift/BAT detections of sGRB precursors, and I use the timing of the observed precursors to place weak constraints on the crust equation of state. I describe how a larger sample of precursor detections could be used alongside coincident gravitational wave detections of the inspiral by Advanced LIGO class detectors to probe the NS structure.