The production of Mg alloy AZ31B sheet in a single deformation step by large-strain extrusion machining (LSEM) is detailed. LSEM imposes intense simple shear in a narrow zone by constrained chip formation. The confined deformation and the associated in situ adiabatic heating are found to be the key factors in production of the Mg sheet without need for external (pre-) heating. A range of shear textures with basal planes inclined to the sheet surface are achieved by this processing. The basal plane inclination could be varied by controlling the strain path. Microstructures, both ultrafine-grained (100-500 nm) and conventional fine-grained (2-5 mu m), have been obtained by controlling the adiabatic heating and the extent of dynamic recrystallization. The LSEM sheet with shear texture and fine grain size shows superior combinations of formability and strength compared to rolled sheet.