Axions are increasingly favoured as a candidate particle for the dark matter in galaxies, since they satisfy the observational requirements for cold dark matter and are theoretically well mo- tivated. Fluctuations in the axion field give rise to stable localised overdensities known as ax- ion stars, which, for the most massive, compact cases, are potential neutron star mimickers. In principle, there are no fundamental arguments against the multi-messenger observations of GW170817/GRB170817A/AT2017gfo arising from the merger of a neutron star with a neutron star mimicker, rather than from a binary neutron star. To constrain this possibility and better un- derstand the astrophysical signatures of a neutron star–axion star (NSAS) merger, we present in this work a detailed example case of a NSAS merger based on full 3D numerical relativity simula- tions, and give an overview of the many potential observables - ranging from gravitational waves, to optical and near-infrared electromagnetic signals, radio flares, fast radio bursts, gamma ray bursts, and neutrino emission. We discuss the individual channels and estimate to which distances current and future observatories might be able to detect such a NSAS merger. Such signals could con- strain the unknown axion mass and its couplings to standard baryonic matter, thus enhancing our understanding of the dark matter sector of the Universe.