Joule energy loss due to resistive heating is omnipresent in today's electronic devices whereas quantum-mechanical dissipation is largely unexplored. Here, we experimentally observe a suppression of the Joule dissipation in Bi2Te3 due to topologically protected surface states. Instead, a different type of dissipation mechanism is observed by pendulum atomic force microscopy, which is related to single-electron tunnelling resonances into image potential states that are slightly above the Bi2Te3 surface. The application of a magnetic field leads to the breakdown of the topological protection of the surface states and restores the expected Joule dissipation process. Nanomechanical energy dissipation experienced by the cantilever of the pendulum atomic force microscope provides a rich source of information on the dissipative nature of the quantum-tunnelling phenomena on the topological insulator surface, with implications for coupling a mechanical oscillator to the generic quantum material.