We study transport in a voltage-biased superconductor-normal-superconductor (SNS) junction made of semiconducting nanowires with strong spin-orbit coupling, as it transitions into a topological superconducting phase for increasing Zeeman field. Despite the absence of a fractional steady-state ac Josephson current in the topological phase, the dissipative multiple Andreev reflection current Idc at different junction transparencies is particularly revealing. It exhibits unique features related to topology, such as gap inversion, the formation of Majorana bound states and fermion-parity conservation. Moreover, the critical current Ic, which remarkably does not vanish at the critical point where the system becomes gapless, provides direct evidence of the topological transition. © IOP Publishing and Deutsche Physikalische Gesellschaft.