Thermal stress-induced protrusions of copper through-silicon-vias (Cu-TSVs) during thermal processing pose substantial reliability concerns in three-dimensional (3D) system integration. In this study, a phase-field-crystal (PFC) model is used to investigate the protrusions and microstructural evolutions of blind Cu-TSVs under different loading conditions. Protrusions are observed only when the TSVs are under εx, εy, and γxy, whereas no protrusions are observed when the TSVs are subjected to pure shear strains γyx. The simulation results suggest that the grains in the top layer of a TSV contribute more to both the protrusion profile and the protrusion height than the grains in the lower layers. Moreover, the protrusion is larger when the misorientation among the grains is larger and the grain size along the y-direction is smaller. In addition, a phenomenological model linking protrusion and microstructural factors and a visual guide from the viewpoint of plastic flow are provided to understand the origins of Cu-TSV protrusion.