The Dark Matter Particle Explorer (DAMPE) has made significant progress in measuring the fluxes of cosmic rays. These new measurements are pivotal in advancing our understanding of the origins and propagation mechanisms of cosmic rays. The bismuth germanium oxide (BGO) calorimeter plays a crucial role in these measurements, particularly in the precise determination of cosmic ray fluxes. However, for a calorimetric experiment like DAMPE, uncertainties in hadronic models persist as a major barrier in achieving more accurate measurements of fluxes of cosmic ray nuclei. This study centers on the measurement of the inelastic hadronic cross sections of carbon and oxygen nuclei interacting BGO crystals target over an extensive energy range, spanning from 200 GeV to 10 TeV. For carbon nuclei interacting with the BGO target. The measurements of the cross sections have achieved a total relative uncertainty of less than 10% below 8 TeV for carbon, and below 3 TeV for oxygen. For oxygen nuclei, the same level of precision was attained below 3 TeV. Additionally, we compare the experimental results with $\mathrm{Geant4}$ and $\mathrm{FLUKA}$ simulations to validate the accuracy and consistency of these simulation tools. Through comprehensive analysis of the inelastic hadronic interaction cross sections, this research provides validation for the hadronic interaction models used in DAMPE’s cosmic-ray flux measurements.