Widespread application of lightweight magnesium and titanium alloys sheet is limited mainly because of their poor-workability issues, both in primary processing by rolling and secondary sheet forming. This study describes a hybrid cutting–extrusion process, large-strain extrusion machining (LSEM), for producing sheet and foil. By utilizing a constraining edge placed across from the cutting tool edge, the usual cutting process is transformed into continuous shear-deformation process, wherein the thickness of the sheet at its exit from the deformation zone is directly controlled. The confinement of the deformation field in LSEM enables near-adiabatic heating in the deformation zone. Consequently, external workpiece heating, intrinsic to sheet manufacturing by multistage rolling in alloys of poor workability (e.g., hexagonal close packed (hcp) alloys and cast materials), is minimized. Furthermore, the deformation parameters, such as strain, strain rate, and strain path, can be controlled to refine the microstructure and induce shear-type crystallographic textures that enable enhanced sheet mechanical properties (strength and formability). This application of LSEM is demonstrated using magnesium alloy AZ31B as a model system. Since LSEM is a single-stage process for sheet production, it is potentially attractive in terms of production economics and energy. Implications for process scale-up and control of plastic flow localization are briefly discussed.