Magnesium (Mg) alloys offer significant potential for reducing the weight of transportation equipment, thereby lowering fuel consumption. However, their broader application is hindered by the inherent trade-off between ductility and strength. Developing a multimodal microstructure has emerged as a promising strategy to address this challenge. While severe plastic deformation techniques can achieve such structures, their practical implementation remains limited. This study explores vortex extrusion—a simple and efficient process that imparts both strain and shear—as a means to refine the microstructure of Mg-2Y-1Zn (at.%) alloys containing long-period stacking ordered (LPSO) phases. Extrusions were conducted at 623 K, with a ram speed of 0.1 mm/s, an extrusion ratio of ~14, and die angles (α) of 30°, 60°, and 90°. Vortex extrusion, with a fixed die angle of 60°, was performed by twisting billets at 90° and 180°. Recrystallization was enhanced by increasing die and twist angles. TEM analysis revealed that kink deformation of the LPSO phase acted as nucleation sites for recrystallized grains, which subsequently developed nanolamellae through solute atom rearrangement. The highest hardness and strength under compression were observed at α = 60°, while higher die angles led to strength reduction due to grain coarsening from processing heat. Notably, vortex-extruded material with a 180° twist outperformed conventionally extruded samples in hardness, strength, and elongation. This enhancement is attributed to increased shear strain from vortex extrusion, promoting extensive kink deformation and fine recrystallized grains embedded with solute-rich nanolamellae. These results demonstrate the potential of vortex extrusion as a practical technique for optimizing the mechanical performance of Mg alloys.