The detection of the 11.3 mu m emission feature characteristic of the Si-C stretch in carbon-rich evolved stars reveals that silicon carbide (SiC) dust grains are condensed in the outflows of carbon stars. SiC dust could be a significant constituent of interstellar dust since it is generally believed that carbon stars inject a considerable amount of dust into the interstellar medium (ISM). The presence of SiC dust in the ISM is also supported by the identification of pre-solar SiC grains of stellar origin in primitive meteorites. However, the 11.3 mu m absorption feature of SiC has never been seen in the ISM, and oxidative destruction of SiC is often invoked. In this work, we quantitatively explore the destruction of interstellar SiC dust through oxidation based on molecular dynamics simulations and density functional theory calculations. We find that the reaction of an oxygen atom with SiC molecules and clusters is exothermic and could cause CO-loss. Nevertheless, even if this is extrapolable to bulk SiC dust, the destruction rate of SiC dust through oxidation could still be considerably smaller than the (currently believed) injection rate from carbon stars. Therefore, the lack of the 11.3 mu m absorption feature of SiC dust in the ISM remains a mystery. A possible solution may lie in the currently believed stellar injection rate of SiC (which may have been overestimated) and/or the size of SiC dust (which may actually be considerably smaller than submicron in size).