ABSTRACTDust grains form in the clumpy ejecta of core-collapse supernovae where they are subject to the reverse shock, which is able to disrupt the clumps and destroy the grains. Important dust destruction processes include thermal and kinetic sputtering as well as fragmentation and grain vaporization. In the present study, we focus on the effect of magnetic fields on the destruction processes. We have performed magnetohydrodynamical simulations using AstroBEAR to model a shock wave interacting with an ejecta clump. The dust transport and destruction fractions are computed using our post-processing code Paperboats, in which the acceleration of grains due to the magnetic field and a procedure that allows partial grain vaporization have been newly implemented. For the oxygen-rich supernova remnant Cassiopeia A, we found a significantly lower dust survival rate when magnetic fields are aligned perpendicular to the shock direction compared to the non-magnetic case. For a parallel field alignment, the destruction is also enhanced but at a lower level. The survival fractions depend sensitively on the gas density contrast between the clump and the ambient medium and on the grain sizes. For a low-density contrast of 100, e.g. 5 nm silicate grains are completely destroyed while the survival fraction of $1\,\mu{\rm m}$ grains is 86 per cent. For a high-density contrast of 1000, 95 per cent of the 5 nm grains survive while the survival fraction of $1\,\mu{\rm m}$ grains is 26 per cent. Alternative clump sizes or dust materials (carbon) have non-negligible effects on the survival rate but have a lower impact compared to density contrast, magnetic field strength, and grain size.