The cross-sections of relativistic deuteron reactions on natural copper were studied in detail by means of activation method. The copper foils were irradiated during experiments with the model spallation targets in the Joint Institute for Nuclear Research. The irradiation of activation samples was performed by beams in the energy range from 1 to 8 GeV. Residual nuclides were measured by the gamma spectrometry. While the EXFOR database contains sets of data for relativistic proton reactions, data for deuteron reactions in this energy range are almost missing. Lack of such experimental cross-section values prevents the use of copper foils from beam integral monitoring. For this reason our experiments focused on their measurement and completely new data were obtained in the energy region where no experimental data have been available so far. The copper monitors with their low sensitivity to fast neutrons will contribute to improvement of the beam integral determination during accelerator-driven system studies.