The effects of forward extrusion as well as extrusion combined with reversible torsion (KoBo extrusion), followed by additional deformation via the MaxStrain module of the Gleeble thermomechanical simulator, on the microstructure, mechanical properties, and electrical conductivity of a Cu-0.7Mg (wt.%) alloy, were investigated. The simulation results highlighted the critical influence of processing history on determining the equivalent strain distribution. The sample subjected to forward extrusion at 400 °C and subsequent MaxStrain processing (FM sample), possessed 76% lower grain size compared to the sample processed solely with MaxStrain (AM sample). Likewise, the KoBo-extruded and MaxStrain-processed sample (KM sample) exhibited 66% smaller grain size compared to the AM sample. Tensile test results revealed that the AM, FM, and KM samples, respectively, possessed 251%, 288%, and 360% higher yield strength, and 95%, 121%, and 169% higher tensile strength compared to the initial annealed alloy, as a result of grain refinement as well as deformation strengthening. Finally, the electrical conductivity measurements revealed that AM, FM, and KM samples, respectively, possessed electrical conductivity values of 37.9, 35.6, and 32.0 MS/m, which, by considering their mechanical properties, makes them eligible to be categorized as high-strength and high-conductivity copper alloys.