The deformation field in machining was controlled to access a range of deformation parameters—strains of 1–15, strain rates of 10–100,000 s−1 and temperatures of up to 0.4 Tm—in the severe plastic deformation (SPD) of copper. This range is far wider than has been accessed to date in conventional SPD methods, enabling a study of the interactive effects of the parameters on microstructure and strength properties. Nano-twinning was demonstrated at strain rates as small as 1000 s−1 at −196 °C and at strain rates of ⩾10,000 s−1 even when the deformation temperature was well above room temperature. Bi-modal grain structures were produced in a single stage of deformation through in situ partial dynamic recrystallization. The SPD conditions for engineering specific microstructures by deformation rate control are presented in the form of maps, both in deformation parameter space and in terms of the Zener–Hollomon parameter.