We present a spin-uncompensated driven Liouville-von Neumann methodology within the time-dependent density functional theory (DLvN-TDDFT) framework to model collinear electron spin transport in open quantum systems. After introducing and validating the approach, through benchmark simulations of spin-polarized transport in simple molecular junctions, we apply it to a magnetic zigzag graphene nanoribbon junction model under external electric fields. The simulations reveal rich spinresolved current dynamics, highlighting the DLvN-TDDFT framework as a promising tool for exploring dynamical spintronic phenomena in low-dimensional open quantum systems.