The microstructural investigation, mechanical properties, and accumulation and dissipation of energies of the magnesium alloy Mg-2.9Y-1.3Nd in the recrystallized state and after severe plastic deformation (SPD) by extrusion are presented. The use of SPD provides the formation of a bimodal structure consisting of grains with an average size 15 µm and of ultrafine-grained grains with sizes less than 1 µm and volume fractions up to 50%, as well as of the fine particles of the second Mg24Y5 phases. It is established that grain refinement during extrusion is accompanied by an increase of the yield strength, increase of the tensile strength by 1.5 times, and increase of the plasticity by 1.8 times, all of which are due to substructural hardening, redistribution of the phase composition, and texture formation. Using infrared thermography, it was revealed that before the destruction of Mg-2.9Y-1.3Nd in the recrystallized state, there is a sharp jump of temperature by 10 °C, and the strain hardening coefficient becomes negative and amounts to (−6) GPa. SPD leads to a redistribution of thermal energy over the sample during deformation, does not cause a sharp increase in temperature, and reduces the strain hardening coefficient by 2.5 times.