A novel motion planning algorithm for robotic bush trimming is presented. The algorithm is based on an optimal route search over a graph. Differently from other works in robotic surface coverage, it entails both accuracy in the surface sweeping task and smoothness in the motion of the robot arm. The proposed method requires the selection of a custom objective function in the joint space for optimal node traversal scheduling, as well as a kinematically constrained time interpolation. The algorithm was tested in simulation using a model of the Jaco arm and three target bush shapes. Analysis of the simulated motions showed how, differently from classical coverage techniques, the proposed algorithm is able to ensure high tool positioning accuracy while avoiding excessive arm motion jerkiness. It was reported that forbidding manipulation posture changes during the cutting phase of the motion is a key element for task accuracy, leading to a decrease of the tool positioning error up to 90%. Furthermore, the algorithm was validated in a real-world trimming scenario with boxwood bushes. A target of 20 mm accuracy was proposed for a trimming result to be considered successful. Results showed that on average 82% of the bush surface was affected by trimming, and 51% of the trimmed surface was cut within the desired level of accuracy. Despite the fact that the trimming accuracy turned out to be lower than the stated requirements, it was found out this was mainly a consequence of the inaccurate, early stage vision system employed to compute the target trimming surface. By contrast, the trimming motion planning algorithm generated trajectories that smoothly followed their input target and allowed effective branch cutting.