Important astrophysical sources, such as gamma-ray bursts (GRBs) or tidal disruption events, are impulsive – strongly varying with time. These outflows are likely highly magnetized near the central source, but their interaction with the external medium is not yet fully understood. Here I consider the combined impulsive magnetic acceleration of an initially highly magnetized shell of plasma and its deceleration by the external medium. I find four main dynamical regimes that (for a given outflow) depend on the external density. (I) For small enough external densities the shell becomes kinetically dominated before it is significantly decelerated, thus reverting to the familiar unmagnetized ‘thin shell’ case, which produces bright reverse shock emission that peaks well after the prompt GRB. (II) For larger external densities the shell remains highly magnetized and the reverse shock is strongly suppressed. It eventually transfers most of its energy through pdV work to the shocked external medium, whose afterglow emission peaks on a time-scale similar to the prompt GRB duration. (III) For even larger external densities there is no initial impulsive acceleration phase. (IV) For the highest external densities the flow remains Newtonian.