The catalytic reduction of CO₂ to produce syngas (CO₂RR-to-syngas) gives a practicable way to utilize CO₂. However, the scale relationships between the adsorption energies of the CO₂ reduction intermediates severely restrict the catalytic performance of catalysts. Herein, we design Cu–M bimetal catalysts (BMCs) to break through the stubborn restriction of scaling relationships on catalytic activity. Density functional theory (DFT) was used to investigate the CO₂RR activity of Cu-based BMCs. It is found that the dual-atom sites (Cu site and M site) result in noteworthy deviations for the scaling relationships between COOH* and CO*. The Cu–Cr catalyst shows the best CO₂RR activity towards CO production. Specifically, only a low overpotential of 0.326 V is required to enable CO₂ reduction to CO. The Cu–Rh catalyst shows a good HER activity due to the lower absolute value. The electrons entering the antibonding orbital significantly increase the Pauli repulsion, which weakens the adsorption energy of atomic hydrogen on the catalysts. The d-band center (ε_d) is not a good descriptor for the HER and CO₂RR over BMCs. Cu–W and Cu–Mo have comparable reaction free energies of the first step involved in the HER and CO₂RR processes, and are expected to be the most suitable catalysts for CO₂RR-to-syngas.