In this work, Al–Mg alloys fabricated by combining continuous rheo-extrusion (CRE) and Sc modification were proposed for producing Al–Mg alloys with high efficiency and superior mechanical performance. The microstructural evolution and mechanical property response of the CREed Al–5Mg alloy with Sc modification were investigated. The grain refinement and strengthening mechanisms induced by nanoscale Al3Sc-phase particles in the alloy were discussed. The results showed that an obvious grain refinement effect was achieved in the CREed Al–5Mg alloy as the Sc content increased from 0 to 0.5 wt%, and the average grain size decreased from 52.6 μm to 2.4 μm, respectively. The primary Al3Sc-phase particles formed during solidification behaved as heterogeneous nucleation sites for the α-Al matrix, while the nanoscale Al3Sc-phase particles achieved during CRE enhanced the driving force of continuous dynamic recrystallization and the Zener drag force. As a result, a superior grain refinement effect was observed. The ultimate tensile strength, yield strength, and hardness of the alloy were enhanced as the Sc content increased from 0 to 0.5 wt%. Grain boundary strengthening, second-phase strengthening, and dislocation strengthening were the main strengthening mechanisms of the CREed Al–Mg–Sc alloys.