Raman MicroSpectroscopy (RMS) is a powerful label-free tool to probe the effects of drugs at a cellular/subcellular level. It is important, however, to be able to extract relevant biochemical and kinetic spectroscopic signatures of the specific cellular responses. In the present study, a combination of Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and Principal Component Analysis (PCA) is used to analyse the RMS data for the example of exposure of primary Oral Squamous Carcinoma Cells (OSCC) to the chemotherapeutic agent cisplatin. Dosing regimens were established by cytotoxicity assays, and the effects of the drug on cellular spectral profiles were monitored from 16 to 72 hours post-exposure using an apoptosis assay, to establish the relative populations of viable (V), early (EA) and late apoptotic/dead (LA/D) cells after the drug treatment. Based on a kinetic model of the progression from V > EA > D, MCR-ALS regression analysis of the RMS responses was able to extract spectral profiles associated with each stage of the cellular responses, enabling a quantitative comparison of the response rates for the respective drug treatments. Moreover, PCA was used to compare the spectral profiles of the viable cells exposed to the drug. Spectral differences were highlighted in the early stages (16 hours exposure), indicative of the initial cellular response to the drug treatment, and also in the late stages (48–72 hours exposure), representing the cell death pathway. The study demonstrates that RMS coupled with multivariate analysis can be used to quantitatively monitor the progression of cellular responses to different drugs, towards future applications for label-free, in vitro, pre-clinical screening.