UNGG cladding nuclear wastes constitute a huge volume of Mg-based materials that raises economic and safety concerns, particularly due to their radioactivity coupled to the potential generation of H$_2$ gas under deep underground disposal. Their significant decontamination would result in more secure and less expensive storage, with a better containment of the separated long-lived radioisotopes that could enter in a classical channel. Sonication of genuine UNGG cladding materials and simulants at 345 kHz in 0.01 M oxalic acid solution (20 °C) allowed the structuring of their surfaces with the observation of homogeneously distributed craters of 20–40 $\mu$m in diameter. After a thorough characterization and comparison of the ultrasound effects generated at the surface, the various samples were artificially contaminated and characterized before sonication. The complete and rapid sonochemical decontamination of Mg-based materials was then observed, in addition to the removal of the carbon layer promoting corrosion on the inner UNGG cladding. The extension of sonication allows the neo-formed brucite (Mg(OH)$_2$) and zirconium-based phases to accumulate on the surface, thus contributing in a slight but continuous surface recontamination process. This phenomenon results from the re-adsorption of uranyl cations from the solution which can be avoided by optimizing the duration of treatment.