It is a well-known fact that compact gravitating objects admit bound state configurations for massive bosonic fields. In this work we describe a new class of superradiant instabilities of axion bound states in neutron star magnetospheres. The instability arises from the mixing of axion and photon modes in the magnetic field of the neutron star which extract energy from the rotating magnetosphere. Unlike for black holes, where the dissipation required for superradiance is provided by an absorbative horizon, the non-hermitian dynamics in this work come from the resistivity in the stellar magnetosphere arising from a finite bulk conductivity.