We report electron-beam activated motion of a catalytic nanoparticle along a graphene step edge and associated etching of the edge. The catalytic hydrogenation process was observed to be activated by a combination of elevated temperature and electron beam irradiation. Reduction of beam fluence on the particle was sufficient to stop the process, leading to the ability to switch on and off the etching. Such an approach enables the targeting of individual nanoparticles to induce motion and beam-controlled etching of matter through activated electrocatalytic processes. The applications of electron-beam control as a paradigm for molecular-scale robotics are discussed.