A novel modeling approach of tumor growth and response to radiotherapy is presented and tested on cervical cancer patient data. A patient-specific mathematical model is developed to predict the evolution of cancer volume at a macroscopic scale, during fractionated external radiotherapy. The model provides estimates of the re-growth of the active portion of the tumor along with their impairment due to irradiation using the linear-quadratic model. At the same time, it accounts for the necrotic portion dynamics by means of an exponential decay to mimic the dead-cell reabsorption. Moreover, the mathematical framework incorporates the interplay between tumor regression rate and radio-sensitivity, as a function of the tumor oxygenation level. Model parameters were estimated by minimizing the difference between predicted and measured tumor volumes, these latter being obtained from a set of 154 serial cone-beam computed tomography (CBCT) scans acquired on 16 patients along the course of the therapy. The model was able to fit very different tumor volume evolutions with an average prediction error lower than 5%. Among all model parameters, the dead-cell removal half-time turned out to be a discriminating parameter between two different patterns of tumor response to irradiation since patients featuring larger values exhibited only a partial volume reduction. The comparison with a simpler model demonstrated an improvement in fitting properties due to the inclusion of the radio-sensitivity dynamics through time as a function of oxygenation. While further analysis is mandatory, we can argue that microenvironment conditions, estimated at planning time, can be useful to refine inclusion criteria based on traditional cell histology and staging of the tumor.