The suppression of spurious events in the region of interest for neutrinoless double beta decay will play a major role in next generation experiments. The background of detectors based on the technology of cryogenic calorimeters is expected to be dominated by α particles, that could be disentangled from double beta decay signals by exploiting the difference in the emission of the scintillation light. CUPID-0, an array of enriched Zn 82 Se scintillating calorimeters, is the first large mass demonstrator of this technology. The detector started data-taking in 2017 at the Laboratori Nazionali del Gran Sasso with the aim of proving that dual read-out of light and heat allows for an efficient suppression of the α background. In this paper we describe the software tools we developed for the analysis of scintillating calorimeters and we demonstrate that this technology allows to reach an unprecedented background for cryogenic calorimeters.