Multiple myeloma (MM) is a malignancy characterized by accumulation of malignant plasma cells within the bone marrow (BM). MM is considered mostly without definitive treatment because of the inability of standard of care therapies to overcome drug-resistant relapse. Genotoxic agents are used in the treatment of MM and exploit the fact that DNA double-strand breaks are highly cytotoxic for cancer cells. However, their mutagenic effects are well-established and described. According to these effects, chemotherapy could cause harmful DNA damage associated with new driver genomic abnormalities providing selective advantage, drug resistance, and higher relapse risk. Several mechanisms associated with MM cell (MMC) resistance to genotoxic agents have been described, underlining MM heterogeneity. The understanding of these mechanisms provides several therapeutic strategies to overcome drug resistance and limit mutagenic effects of treatment in MM. According to this heterogeneity, adopting precision medicine into clinical practice, with the development of biomarkers, has the potential to improve MM disease management and treatment.