Even several thousands of DNA lesions are induced in one cell within one day. DNA damage may lead to mutations, formation of chromosomal aberrations, or cellular death. A particularly cytotoxic type of DNA damage is single- and double-strand breaks (SSBs and DSBs, respectively). In this work, we followed DNA conformational transitions induced by the disruption of DNA backbone. Conformational changes of chromatin in living cells were induced by a bleomycin (BLM), an anticancer drug, which generates SSBs and DSBs. Raman micro-spectroscopy enabled to observe chemical changes at the level of single cell and to collect hyperspectral images of molecular structure and composition with sub-micrometer resolution. We applied multivariate data analysis methods to extract key information from registered data, particularly to probe DNA conformational changes. Applied methodology enabled to track conformational transition from B-DNA to A-DNA upon cellular response to BLM treatment. Additionally, increased expression of proteins within the cell nucleus resulting from the activation of repair processes was demonstrated. The ongoing DNA repair process under the BLM action was also confirmed with confocal laser scanning fluorescent microscopy.