This paper focuses on an integrated approach to study the materials and the degradation issues in the urban mural painting Ama Il Tuo Sogno, painted by the famous street artist Jorit Agoch in Matera (Italy). The study was conducted in the framework of a conservation project, aiming to contrast a progressive decay affecting the artifact that started a few months after its creation. Multi-analytical techniques were used to investigate the stratigraphy and chemical composition of the pictorial film within a low-impact analytical protocol for sustainable diagnostics. They included polarized light microscopy in UV and VIS reflected light, FTIR spectroscopy, Py-GC-HRAMS, and SEM-EDS. The mineralogical–petrographic composition of the mortar employed in the pictorial support was also studied with optical microscopy of thin sections and X-ray diffractometry. To know the mechanism underlying the degradation, IR thermography was performed in situ to establish the waterways and the distribution of the humidity in the mural painting. In addition, ion chromatography and X-ray diffractometry were used to identify and quantify the soluble salts and to understand their sources. The overall results allowed us to determine the chemical composition of the binder and pigments within the pictorial layers, the mineralogical–petrographic characteristics of the mortar of the support, and the execution technique of the painting. They also highlighted a correlation between the presence of humidity in the painted mural and the salt damage. The mineralogical phases were detected in the mural materials by XRD, and the results of ion chromatographic analyses suggested a supply of soluble salts mainly from the mortar of the support. Finally, the study provided basic knowledge for planning appropriate sustainable conservation measures.