CUPID-Mo, located in the Laboratoire Souterrain de Modane (France), was a demonstrator for the next generation 0 νββ decay experiment, CUPID. It consisted of an array of 20 enriched Li 2100 MoO 4 bolometers and 20 Ge light detectors and has demonstrated that the technology of scintillating bolometers with particle identification capabilities is mature. Furthermore, CUPID-Mo can inform and validate the background prediction for CUPID. In this paper, we present a detailed model of the CUPID-Mo backgrounds. This model is able to describe well the features of the experimental data and enables studies of the 2 νββ decay and other processes with high precision. We also measure the radio-purity of the Li 2100 MoO 4 crystals which are found to be sufficient for the CUPID goals. Finally, we also obtain a background index in the region of interest of 3.7 -0.8+0.9 (stat) -0.7+1.5 (syst) ×10-3 counts/ Δ EFWHM/ mol iso/ year , the lowest in a bolometric 0 νββ decay experiment.