Chip formation in conventional cutting occurs by deformation that is only partially bounded by the cutting tool. The unconstrained free surface is a complication in determining the deformation of chip formation. The constrained cutting employs a constraining tool in the cutting process to confine the otherwise free surface and enable direct control of the chip formation deformation. A study has been made on the deformation mechanics of plane-strain constrained cutting using high speed imaging and digital image correlation (DIC) methods. For different constrained levels (including unconstrained free cutting), material flow of chip formation is directly observed; strain rate and strain in the chip as well as the subsurface region are quantified; cutting forces are measured; and surface finish are examed. The study shows that chip formation in constrained cutting can occur in two different deformation modes, i.e., simple shear and complex extrusion, depending on the constrained level. Constrained cutting in simple shear regime can reduce strain, reduce cutting force and energy, and improve surface finish compared to free cutting, therefore it is more efficient for material removal than free cutting. Constrained cutting in the complex extrusion regime imposes a significant amount of surface / subsurface deformation and consumes a very high cutting energy, and therefore is not suitable for material removal. Furthermore, the mechanics of chip formation in both free cutting and constrained cutting, especially the roles played by the free surface and the constraining tool, are discussed.