We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e. a perfectly reflecting mirror) in flat spacetime. For Taub-NUT spacetime with positive 2-space curvature, $\varepsilon = +1$, we demonstrate that the particle and energy spectra is thermal at late-times and that particle production is suppressed by the NUT parameter. We derive a new class of mirror trajectories corresponding to a time-reversed Taub-NUT spacetime with vanishing 2-space curvature, $\varepsilon = 0$, where early-time thermality and a non-monotonic dependence on the NUT parameter are demonstrated. We also compute the radiation spectrum in the rotating, electrically charged (Kerr-Newman) Taub-NUT scenario, and the extremal case, showing explicitly how these parameters affect the outgoing particle and energy fluxes.