Trajectory-based simulations of transport in porous and fractured media are computationally fast, straight-forward to parallelize, and do not introduce additional numerical dispersion. This makes them an attractive alternative to traditional Eulerian numerical solutions of the advection-dispersion-reaction equation. An accurate simulation of many processes in geological media requires a coupled representation of fluid flow, heat transport, and mechanical deformation. Typically, these physical processes are monolithically coupled by making use of finite element methods. Reasons for this are the relative ease to implement the coupling of different physical processes via finite elements, their ability to natively handle full material tensors and unstructured grids, as well as their matureness and common usage in solving problems from structural mechanics. While finite elements yield a continuous solution of the primary unknown, unfortunately, they yield Darcy velocity fields which are neither conforming nor element-wise mass conservative leading to a jump of the Darcy velocity normal to an element interface. However, a locally mass-conservative velocity field in elements or patches of a dual grid as well as a continuous average Darcy velocity normal to the control-volume interfaces are necessary prerequisites for accurate and consistent particle tracking. To overcome this challenge, we adapt the flux projection of Selzer and Cirpka (2020), initially presented for steady-state groundwater flow, for coupled thermo-hydro-mechanical models based on Galerkin-type finite elements, thus yielding a conforming and element-wise mass-conservative Darcy velocity field via postprocessing. Based on this, we use the semi-analytical particle-tracking scheme presented by Selzer et al. (2021) to compute trajectories. We couple this framework to OpenGeoSys, which is an open-source multi-physics simulation platform based on finite elements, and apply it to a three-dimensional thermo-hydro-mechanical model including several geological layers simulating the fate of a conceptually simplified deep geological waste repository for high-level nuclear waste in clay stone as host-rock formation over one million years including glacial cycles.