A commercially pure Cu and a Cu-8 wt.%Sn alloy were subjected to high pressure torsion (HPT) to study the effect of Sn as solute element and deformation rate on the grain refinement mechanism and the defect accumulation in Cu. The microstructure and hardness of produced ultrafine grained (UFG) states of both materials were carefully characterized. We show that addition of Sn in Cu leads to significant decrease in grain size, accumulation of higher stored energy and increase in hardness accompanied with the delay of hardness saturation with shear strain. Increasing HPT deformation rate induces significant heat dissipation in the processed materials markedly pronounced in CuSn8 as compared to Cu. Surprisingly, deformation rate has the opposite effect on the microhardness of UFG Cu and CuSn8, which decreases with the deformation rate for the case of Cu, while exhibits faster saturation to higher values for CuSn8. We also show that despite higher self-heating at higher deformation rates, higher HPT rotation speed provides reduction in grain size and increase in the defect density for CuSn8 alloy. This effect is assumed to be related to strong interactions between Sn solute atoms and strain-induced defects so that mechanically driven effects prevail over dynamic annihilation of dislocations. Finally, we present a qualitative model based on the phenomena of production and annihilation of dislocations. This model was able to reproduce the evolution of grain size, concentrations defects and hardness with different deformation parameters and after the addition of solute element in material.