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Cadmium arsenide Cd$_3$As$_2$ hosts massless Dirac electrons in its ambient-conditions tetragonal phase. We report X-ray diffraction and electrical resistivity measurements of Cd$_3$As$_2$ upon cycling pressure beyond the critical pressure of the tetragonal phase and back to ambient conditions. We find that at room temperature the transition between the low- and high-pressure phases results in large microstrain and reduced crystallite size both on rising and falling pressure. This leads to non-reversible electronic properties including self-doping associated with defects and a reduction of the electron mobility by an order of magnitude due to increased scattering. Our study indicates that the structural transformation is sluggish and shows a sizable hysteresis of over 1~GPa. Therefore, we conclude that the transition is first-order reconstructive, with chemical bonds being broken and rearranged in the high-pressure phase. Using the diffraction measurements we demonstrate that annealing at ~200$^\circ$C greatly improves the crystallinity of the high-pressure phase. We show that its Bragg peaks can be indexed as a primitive orthorhombic lattice with a_HP~8.68 A b_HP~17.15 A and c_HP~18.58 A. The diffraction study indicates that during the structural transformation a new phase with another primitive orthorhombic structure may be also stabilized by deviatoric stress, providing an additional venue for tuning the unconventional electronic states in Cd3As2.