A Single-crystal Diamond (SD) detector prototype was installed at Joint European Torus (JET) in 2013 and the achieved results have shown its spectroscopic capability of measuring 2.5 MeV neutrons from deuterium plasmas. This paper presents measurements of the SD response function to monoenergetic neutrons, which is a key point for the development of a neutron spectrometer based on SDs and compares them with Monte Carlo simulations. The analysis procedure allows for a good reconstruction of the experimental results. The good pulse height energy resolution (equivalent FWHM of 80 keV at 2.5 MeV), gain stability, insensitivity to magnetic field, and compact size make SDs attractive as compact neutron spectrometers of high flux deuterium plasmas, such as for instance those needed for the ITER neutron camera.