The thermal deformation behavior of the Mg–Gd–Y–Zr–Ag alloy was studied by isothermal hot compression tests at high temperatures. The flow stress increased with increased strain rates and decreased temperatures, first increasing and finally remaining stable with increased strain. A hot processing map was built. Using the processing map and microstructural analysis, the temperature should remain at 673–773 K for this alloy to ensure the deformation quality. The primary softening mechanism is discontinuous dynamic recrystallization (DDRX). Rising temperatures and declining strain rates facilitated the emergence and growth of Dynamic recrystallization (DRX) grains. An original JC (O–JC) model and a modified JC (M–JC) model were established. The M–JC model indicated a better prediction than the O–JC model. Still, it was deficient in predicting flow stresses with insufficient coupling effects. Hence, based on the M–JC model, a newly modified JC (NM–JC) model, which further enhances the interaction between strain and strain rate as well as strain and temperature, is proposed. Its projected values can better align with the tested values.