The effect of rotary swaging on the microstructure, texture, and mechanical properties of the magnesium alloy Mg-4.4Al-0.9Zn-0.4Mn is studied. Repetitive processing, conducted at progressively dropped deformation temperature (from 400 down to 200 °C), leads to an increase in the cumulative strain ε. Rotary swaging of the alloy is shown to lead to microstructure fragmentation due to intensive twinning on various crystallographic planes. A high density of twins observed at the final stage of deformation, at ε = 2.77, leads to a decrease in the distance between boundaries (including both twins and grain boundaries) to ≈3 μm. With decreasing temperature, 0.2-μm-wide secondary deformation twins form within the primary twins with a width in the range of 1.5–2.5 μm. The texture analysis shows that, upon deformation, the number of orientations increases as does their scatter. Rotary swaging at 350 °C to ε = 2.77 gives rise to an increase of both strength and tensile ductility of the alloy. The high strength characteristics are achieved due to the formation of a subgrain structure and profuse twinning. The increased tensile ductility is associated with the activation of prismatic slip in addition to developed basal slip.