  The gravitational-wave signal from the merger of two neutron stars cannot be
easily differentiated from the signal produced by a comparable-mass mixed
binary of a neutron star and a black hole. Indeed, both binary types can
account for the gravitational-wave signal GW170817 even if its electromagnetic
counterpart emission is taken into account. We propose a method that {requires
neither information from the post-inspiral phase of the binary nor an
electromagnetic counterpart} to identify mixed binaries of neutron stars
merging with low-mass black holes using gravitational-waves alone. This method
is based on the fact that certain neutron star properties that can be measured
with gravitational-waves are common or similar for all neutron stars. For
example all neutron stars share the same equation of state and if the latter is
hadronic, neutron stars have similar radii. If a mixed binary is misidentified
as a neutron star binary, the inferred neutron star properties will be
misestimated and appear as outliers in a population of low-mass binaries. We
show that as few as $\sim 5$ low-mass events will allow for the identification
of the type of one event at the $80\%$ confidence level. We model the
population of low-mass binaries with a hierarchical mixture model and show that
we can constrain the existence of mixed binaries or measure their abundance
relative to neutron star binaries to $\sim 0.1$ at the $68\%$ credible level
with 100 events.
