  We present GRaM-X (General Relativistic accelerated Magnetohydrodynamics on
AMReX), a new GPU-accelerated dynamical-spacetime general relativistic
magnetohydrodynamics (GRMHD) code which extends the GRMHD capability of
Einstein Toolkit to GPU-based exascale systems. GRaM-X supports 3D adaptive
mesh refinement (AMR) on GPUs via a new AMR driver for the Einstein Toolkit
called CarpetX which in turn leverages AMReX, an AMR library developed for use
by the United States DOE's Exascale Computing Project (ECP). We use the Z4c
formalism to evolve the equations of GR and the Valencia formulation to evolve
the equations of GRMHD. GRaM-X supports both analytic as well as tabulated
equations of state. We implement TVD and WENO reconstruction methods as well as
the HLLE Riemann solver. We test the accuracy of the code using a range of
tests on static spacetime, e.g. 1D MHD shocktubes, the 2D magnetic rotor and a
cylindrical explosion, as well as on dynamical spacetimes, i.e. the
oscillations of a 3D TOV star. We find excellent agreement with analytic
results and results of other codes reported in literature. We also perform
scaling tests and find that GRaM-X shows a weak scaling efficiency of $\sim
40-50\%$ on 2304 nodes (13824 NVIDIA V100 GPUs) with respect to single-node
performance on OLCF's supercomputer Summit.
