Twin boundaries (TBs) play an essential role in enhancing the mechanical, electronic and transport properties of polycrystalline materials. However, the mechanisms are not well understood. In particular, we considered that they may play an important role in boron very rich boron carbide (BvrBC), which exhibits such promising properties as low density, super hardness, high abrasion resistance, and excellent neutron absorption. Here, we apply first-principles-based simulations to identify the atomic structures of TBs in BvrBC and their roles for the inelastic response to applied stresses. In addition to symmetric TBs in BvrBC, we identified a new type of asymmetric twin that constitutes the phase boundaries between boron rich boron carbide (B13C2) and BvrBC (B14C). The predicted mechanical response of these asymmetric twins indicates a significant reduction of the ideal shear strength compared to single crystals B13C2 and B14C, suggesting that the asymmetric twins facilitate the disintegration of icosahedral clusters under applied stress, which in turn leads to amorphous band formation and brittle failure. These results provide a mechanistic basis towards understating the roles of TBs in BvrBC and related superhard ceramics.