A rapidly spinning magnetar in a young supernova (SN) can produce a superluminous transient by converting a fraction of its rotational energy into radiation. Here, we present the first three-dimensional hydrodynamical simulations ever performed of a magnetar-powered SN in the circumstellar medium formed by the ejection of the outer layers of the star prior to the blast. We find that hydrodynamical instabilities form on two scales in the ejecta, not just one as in ordinary core-collapse SNe: in the hot bubble energized by the magnetar and in the forward shock of the SN as it plows up ambient gas. Pressure from the bubble also makes the instabilities behind the forward shock more violent and causes more mixing in the explosion than in normal SNe, with important consequences for the light curves and spectra of the event that cannot be captured by one-dimensional models. We also find that the magnetar can accelerate Ca and Si to velocities of ~ 12000 km/s and account for their broadened emission lines in observations. Our simulations also reveal that energy from even weak magnetars can accelerate iron-group elements deep in the ejecta to 5000-7000 km / s and explain the high-velocity Fe observed at early times in some core-collapse SNe such as SN 1987A.