Gravitational waves from neutron star–black hole (NSBH) mergers that undergo tidal disruption provide a potential avenue to study the equation of state of neutron stars and hence the behavior of matter at its most extreme densities. We present a phenomenological model for the gravitational-wave signature of tidal disruption, which allows us to measure the disruption time. We carry out a study with mock data, assuming an optimistically nearby NSBH event with parameters tuned for measuring the tidal disruption. We show that a two-detector network of 40 km Cosmic Explorer instruments can measure the time of disruption with a precision of ≈0.5 ms, which corresponds to a constraint on the neutron star radius of ≈0.7 km (90% credibility). This radius constraint is wider than the constraint obtained by measuring the tidal deformability of the neutron star of the same system during the inspiral. Moreover, the neutron star radius is likely to be more tightly constrained using binary neutron star mergers. While NSBH mergers are important for the information they provide about stellar and binary astrophysics, they are unlikely to provide insights into nuclear physics beyond what we will already know from binary neutron star mergers.