A new model to describe magnetization of a magnetoactive elastomer (MAE) filled with magnetically hard powder is proposed. The magnetization process is treated as a result of a joint contribution of an assembly of single-domain particles each of which dwells inside its own elastomer cavity. Magnetization of such a particle is a complex magnetomechanical process that combines intrinsic magnetization reversal and particle mechanical rotation. Possible slippage of the particles, in the course of which they disconnect from the matrix and, on their move, rub against the cavity wall, is explicitly taken into account. The influence of the slippage effect on the macroscopic magnetization of the composite is analyzed by means of computer simulation. Occurrence of asymmetrical magnetization loops of single-domain particles located in an elastic medium is demonstrated. It is shown that by allowing for the slippage, it becomes possible to explain the experimentally observed anomalously low but non-zero half-width (coercivity) of the hysteresis loops of the MAE samples.