CUPID-Mo, located in the Laboratoire Souterrain de Modane (France), was a demonstrator for the next generation $$0\nu \beta \beta $$ 0 ν β β decay experiment, CUPID. It consisted of an array of 20 enriched Li$$_{2}$$ 2 $$^{100}$$ 100 MoO$$_4$$ 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 $$2\nu \beta \beta $$ 2 ν β β decay and other processes with high precision. We also measure the radio-purity of the Li$$_{2}$$ 2 $$^{100}$$ 100 MoO$$_4$$ 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 $$^{+0.9}_{-0.8}$$ - 0.8 + 0.9  (stat)$$^{+1.5}_{-0.7}$$ - 0.7 + 1.5  (syst) $$\times ~10 ^{-3}$$ × 10 - 3  counts/$$\Delta E_{\text {FWHM}}/\text {mol}_{\text {iso}}/\text {year},$$ Δ E FWHM / mol iso / year , the lowest in a bolometric $$0\nu \beta \beta $$ 0 ν β β decay experiment.