  We study the high-energy limit of projectable Ho\v rava gravity using
on-shell graviton scattering amplitudes. We compute the tree-level amplitudes
using symbolic computer algebra and analyze their properties in the case of
collisions with zero total momentum. The amplitudes grow with collision energy
in the way consistent with tree-level unitarity. We discuss their angular
dependence and derive the expression for the differential cross section that
happens to depend only on the essential combinations of the couplings. One of
our key results is that the amplitudes for arbitrary kinematics are finite when
the coupling $\lambda$ in the kinetic Lagrangian is taken to infinity -- the
value corresponding to candidate asymptotically free ultraviolet fixed points
of the theory. We formulate a modified action which reproduces the same
amplitudes and is directly applicable at $\lambda=\infty$, thereby establishing
that the limit $\lambda\to\infty$ of projectable Ho\v rava gravity is regular.
As an auxiliary result, we derive the generalized Ward identities for the
amplitudes in non-relativistic gauge theories.
