Reprogramming of cellular metabolism is a driving factor of tumour progression and radiation therapy resistance. Identifying biochemical signatures associated with tumour radioresistance may assist with the development of targeted treatment strategies to improve clinical outcomes. Raman spectroscopy (RS) can monitor post-irradiation biomolecular changes and signatures of radiation response in tumour cells in a label-free manner. Convolutional Neural Networks (CNN) perform feature extraction directly from data in an end-to-end learning manner, with high classification performance. Furthermore, recently developed CNN explainability techniques help visualize the critical discriminative features captured by the model. In this work, a CNN is developed to characterize tumour response to radiotherapy based on its degree of radioresistance. The model was trained to classify Raman spectra of three human tumour cell lines as radiosensitive (LNCaP) or radioresistant (MCF7, H460) over a range of treatment doses and data collection time points. Additionally, a method based on Gradient-Weighted Class Activation Mapping (Grad-CAM) was used to determine response-specific salient Raman peaks influencing the CNN predictions. The CNN effectively classified the cell spectra, with accuracy, sensitivity, specificity, and F1 score exceeding 99.8%. Grad-CAM heatmaps of H460 and MCF7 cell spectra (radioresistant) exhibited high contributions from Raman bands tentatively assigned to glycogen, amino acids, and nucleic acids. Conversely, heatmaps of LNCaP cells (radiosensitive) revealed activations at lipid and phospholipid bands. Finally, Grad-CAM variable importance scores were derived for glycogen, asparagine, and phosphatidylcholine, and we show that their trends over cell line, dose, and acquisition time agreed with previously established models. Thus, the CNN can accurately detect biomolecular differences in the Raman spectra of tumour cells of varying radiosensitivity without requiring manual feature extraction. Finally, Grad-CAM may help identify metabolic signatures associated with the observed categories, offering the potential for automated clinical tumour radiation response characterization.