  Tidal disruption has a dramatic impact on the outcome of neutron star-black
hole mergers. The phenomenology of these systems can be divided in three
classes: nondisruptive, mildly disruptive or disruptive. The cutoff frequency
of the gravitational radiation produced during the merger (which is potentially
measurable by interferometric detectors) is very different in each regime, and
when the merger is disuptive it carries information on the neutron star
equation of state. Here we use semianalytical tools to derive a formula for the
critical binary mass ratio $Q=M_{\rm BH}/M_{\rm NS}$ below which mergers are
disruptive as a function of the stellar compactness $\mathcal{C}=M_{\rm
NS}/R_{\rm NS}$ and the dimensionless black hole spin $\chi$. We then employ a
new gravitational waveform amplitude model, calibrated to $134$ general
relativistic numerical simulations of binaries with black hole spin
(anti-)aligned with the orbital angular momentum, to obtain a fit to the
gravitational-wave cutoff frequency in the disruptive regime as a function of
$\mathcal{C}$, $Q$ and $\chi$. Our findings are important to build
gravitational wave template banks, to determine whether neutron star-black hole
mergers can emit electromagnetic radiation (thus helping multimessenger
searches), and to improve event rate calculations for these systems.
