The use of continuous fiber-reinforced thermoplastics (FRTP) in automotive industry increases due to their excellent material properties and possibility of rapid processing. The scale spanning heterogeneity of their material structure and its influence on the material behavior, however, presents significant challenges for most joining technologies, such as self-piercing riveting (SPR). During mechanical joining, the material structure is significantly altered within and around the joining zone, heavily influencing the material behavior. A comprehensive understanding of the underlying phenomena of material alteration during the SPR process is essential as basis for validating numerical simulations. This study examines the material structure at ten stages of a step-setting test of SPR with two FRTP sheets with glass-fiber reinforcement. Utilizing X-ray computed tomography (CT), the damage phenomena within different areas of the setting test are analyzed three-dimensionally and key parameters are quantified. Dominating phenomena during the penetration of the rivet into the laminate are fiber failure (FF), interfiber failure (IFF) and fiber bending, while delamination, fiber kinking and roving splitting are also observed. At the final stages, the bottom layers of the second sheet collapse and form a bulge into the cavity of the die.