Stars within 0.1 pc of the supermassive black hole Sgr A* at the Galactic centre are expected to encounter a cluster of stellar-mass black holes (BHs) that have segregated to that region. Some of these stars will scatter off an orbiting BH and be kicked out of the Galactic centre with velocities up to 2000 km/sec . We calculate the resulting ejection rate of hypervelocity stars (HVSs) by this process under a variety of assumptions, and find it to be comparable to the tidal disruption rate of binary stars by Sgr A*, first discussed by Hills (1988). Under some conditions, this novel process is sufficient to account for all the B-type HVSs observed in the halo, and to dominate the production rate of all HVSs with lifetimes much less than the relaxation time-scale at a distance 2 pc from Sgr A* (> 2 Gyr). Since HVSs are produced by at least two unavoidable processes, the statistics of HVSs could reveal bimodal velocity and mass distributions, and can constrain the distribution of BHs and stars in the innermost 0.1 pc around Sgr A*.