In this paper, a nonlinear model predictive control (NMPC) policy is developed for kinematically and dynamically coupled rotational-translational motion of a chaser spacecraft relative to an uncooperative, tumbling target asteroid. The goal of the NMPC policy is to rendezvous the chaser spacecraft, equipped with a robotic grasper, to the asteroid surface to collect a sample rock. The relative spacecraft motion model is kinematically coupled due to the non-center-of-mass points on both the target and chaser. Additionally, the chaser spacecraft is actuated by eight gimbaled thrusters, introducing dynamic coupling via control that simultaneously produces forces and torques. The combined 6-degree-of-freedom kinematically and dynamically coupled relative motion model is constrained by the NMPC policy to approach the asteroid surface via a lineof-sight cone, while enforcing thruster gimbal limit constraints. Simulations demonstrate the effectiveness of the NMPC policy in bringing the chaser spacecraft to rest relative the tumbling asteroid while satisfying state and input constraints.