The cleaning of buildings, statues, and artworks composed of stone materials from metal corrosion is an important topic in the cultural heritage field. In this work the cleaning effectiveness of a PVA-PEO-borax hydrogel in removing metal corrosion products from different porosity stones has been assessed by using a multidisciplinary and non-destructive approach based on relaxation times measurement by single-sided portable Nuclear Magnetic Resonance (NMR), Scanning Electron Microscopy—Energy Dispersive Spectroscopy (SEM-EDS), and Raman Spectroscopy. To this end, samples of two lithotypes, Travertine and Carrara marble, have been soiled by triggering acidic corrosion of some copper coins in contact with the stone surface. Then, a PVA-PEO-borax hydrogel was used to clean the stone surface. NMR data were collected in untreated, soiled with corrosion products, and hydrogel-cleaned samples. Raman spectroscopy was performed on PVA-PEO-borax hydrogel before and after cleaning of metal corrosion. Furthermore, the characterization of the dirty gel was obtained by SEM-EDS. The combination of NMR, SEM-EDS and Raman results suggests that the mechanism behind the hydrogel cleaning action is to trap heavy metal corrosion products, such as Cu2+ between adjacent boron ions cross-linked with PVA. Moreover, the PVA-PEO-borax hydrogel cleaning effectiveness depends on the stone porosity, being better in Carrara marble compared to Travertine.