  We develop a formalism for studying the dynamics of massive black hole
binaries embedded in gravitationally-bound stellar cusps, and study the binary
orbital decay by three-body interactions, the impact of stellar slingshots on
the density profile of the inner cusp, and the properties of the ejected
hypervelocity stars (HVSs). We find that the scattering of bound stars shrinks
the binary orbit and increases its eccentricity more effectively than that of
unbound ambient stars. Binaries with initial eccentricities e>0.3 and/or
unequal-mass companions (M_2/M_1<0.1) can decay by three-body interactions to
the gravitational wave emission regime in less than a Hubble time. The stellar
cusp is significantly eroded, and cores as shallow as \rho\propto r^-0.7 may
develop from a pre-existing singular isothermal density profile. A population
of HVSs is ejected in the host galaxy halo, with a total mass ~M_2. We scale
our results to the scattering of stars bound to Sgr A*, the massive black hole
in the Galactic Center, by an inspiraling companion of intermediate mass.
Depending on binary mass ratio, eccentricity, and initial slope of the stellar
cusp, a core of radius ~0.1 pc typically forms in 1-10 Myr. On this timescale
about 500-2500 HVSs are expelled with speeds sufficiently large to escape the
gravitational potential of the Milky Way.
