Motivated by impurity-induced magnetic ordering phenomena in spin-gap materials like TlCuCl₃, we develop a mean-field theory for strongly disordered antiferromagnets, designed to capture the broad distribution of coupling constants in the effective model for the impurity degrees of freedom. Based on our results, we argue that in the presence of random magnetic couplings the conventional first-order spin-flop transition of an anisotropic antiferromagnet is split into two transitions at low temperatures, associated with separate order parameters along and perpendicular to the field axis. We demonstrate the existence of either a bicritcal point or a critical endpoint in the temperature-field phase diagram, with the consequence that signatures of the spin flop are more pronounced at elevated temperature.