In this article, the evolution of defect subsystems and the contribution of Poisson’s ratios in the process of microplastic deformation of auxetic beryllium with the change of temperature and strain amplitude are investigated by means of the method of low-frequency internal friction (LFIF). The velocities of defects in the beryllium are mathematically modelled in different temperature intervals, which include the auxetic and non-auxetic material states. The relations of motion rates of defects, $V/V_{0}$, parameters of slowing-down, $В_{і}$, and activation energies, $Е_{і}$ in beryllium are calculated within the scope of the dislocation—disclination model in a wide temperature range. As shown, theoretically evaluated values well agree with experimentally obtained ones.