Black hole-neutron star ( BHNS ) binary mergers are candidate engines for generating both short-hard gamma-ray bursts ( SGRBs ) and detectable gravitational waves . Using our most recent conformal thin-sandwich BHNS initial data and our fully general relativistic hydrodynamics code , which is now AMR-capable , we are able to efficiently and accurately simulate these binaries from large separations through inspiral , merger , and ringdown . We evolve the metric using the BSSN formulation with the standard moving puncture gauge conditions and handle the hydrodynamics with a high-resolution shock-capturing scheme . We explore the effects of BH spin ( aligned and anti-aligned with the orbital angular momentum ) by evolving three sets of initial data with BH : NS mass ratio q = 3 : the data sets are nearly identical , except the BH spin is varied between a / M _ { BH } = -0.5 ( anti-aligned ) , 0.0 , and 0.75 . The number of orbits before merger increases with a / M _ { BH } , as expected . We also study the nonspinning BH case in more detail , varying q between 1 , 3 , and 5 . We calculate gravitational waveforms for the cases we simulate and compare them to binary black-hole waveforms . Only a small disk ( < 0.01 M _ { \odot } ) forms for the anti-aligned spin case ( a / M _ { BH } = -0.5 ) and for the most extreme mass ratio case ( q = 5 ) . By contrast , a massive ( M _ { disk } \approx 0.2 M _ { \odot } ) , hot disk forms in the rapidly spinning ( a / M _ { BH } = 0.75 ) aligned BH case . Such a disk could drive a SGRB , possibly by , e.g. , producing a copious flux of neutrino-antineutino pairs .