Friction Stir Welding (FSW) is a solid-state joining process in which workpieces are welded together using a non-consumable pin-tool that rotates and moves along the interface. The joining is due to heat generated by friction between the tool and the material. The simulation of FSW processes is a valuable tool for predicting material flow, temperature distributions, tool reaction forces, metallurgy, and possible weld defects. The goal is to help industrial applicants optimize process parameters and produce better-quality welds. Friction Stir Welding is a highly coupled, thermo-mechanical problem that can be described in both Eulerian and Lagrangian frameworks. The benefit of using an Eulerian framework is that it prevents the need for frequent re-meshing, allows for the use of simpler thermo-visco-plastic constitutive laws, and leads to more efficient and robust simulations. A drawback of the Eulerian framework is the inability to keep the mesh undeformed when using non-rotationally symmetric tools in conjunction with non-zero tilt angles, which are both essential for industrial applications. The presented approach addresses this issue by modeling the tool-workpiece interface using CutFEM, leading to a regular, non-body-fitted mesh with undeformed elements. This allows for arbitrary tool geometries and movement. Stabilization techniques are required to address incompressible material behavior, a convection-dominated thermal problem (both Orthogonal Subgrid-Scales), and small cut instabilities (Ghost Penalty). The developed FE framework directly reads and processes CAD files (STEP/IGES/STL) of pin-tools and computes a discrete level-set function, on which the CutFEM algorithm is based. Consequentially, pre-processing efforts are greatly reduced, especially when frequently modifying tool geometries. The simulation results agree well with the experimental data (temperature evolution and reaction forces), and a parameter study is carried out to further investigate the influence of different process parameters.