Disulfiram (DSF) and its derivatives were here investigated as antineoplastic agents, and their important feature is the ability to influence the UPS. We have recently shown that hydroxocobalamin catalyzes the aerobic oxidation of diethyldithiocarbamate to form disulfiram and its oxy-derivatives (DSFoxy; i.e., sulfones and sulfoxides), which induce cytoplasm vacuolization and paraptosis-like cancer cell death. We used LC-MS/MS and bioinformatics analysis to determine the key points in these processes. DSFoxy was found to induce an increase in the number of ubiquitinated proteins, including oxidized ones, and a decrease in the monomeric ubiquitin. Enhanced ubiquitination was revealed for proteins involved in the response to exogenous stress, regulation of apoptosis, autophagy, DNA damage/repair, transcription and translation, folding and ubiquitination, retrograde transport, the MAPK cascade, and some other functions. The results obtained indicate that DSF oxy-derivatives enhance the oxidation and ubiquitination of many proteins regulating proteostasis (including E3 ligases and deubiquitinases), which leads to inhibition of protein retrotranslocation across the ER membrane into the cytosol and accumulation of misfolded proteins in the ER followed by ER swelling and initiates paraptosis-like cell death. Our results provide new insight into the role of protein ubiquitination/deubiquitination in regulating protein retrotranslocation across the ER membrane into the cytosol and paraptosis-like cell death.