The present manuscript documents the development of a practical calculation scheme to model the response of a diamond detector in the mixed (neutron and gamma) radiation field of the CROCUS experimental reactor at EPFL. The model is shown to perform reasonably well in terms of energy spectra shapes for the limited amounts of irradiations considered; the relative magnitude of the neutron and gamma contributions to the detector output is, however, not properly captured. The gamma contribution is underestimated by a factor of four if the neutron contribution is correctly captured. A sensitivity study to three parameters (the azimuthal position of the detector, the magnitude of the neutron and gamma sources, and the threshold voltage used in the detector) is also carried out to analyze the effect of modeling assumptions and experimental choices on the results. Then, a detailed analysis of the computational results is carried out to provide quantitative information about the response of a diamond detector in a mixed radiation field. It is shown that the low-energy interactions are mainly produced by gamma interactions; that the high energy interactions are generated by proton recoil interactions; and that 60% of the recorded neutron interactions are produced by thermal neutron captures in Li-6, while the rest come from scattering interactions with fast neutrons. Finally, it is demonstrated that considering some of the effects of the electronics on the pulses (RC time constant) is required to reproduce the trends observed in the experimental results, especially the increased detection rate within the diamond crystal.