In the relativistic mean field approximation, the relativistic energy losses of the direct Urca processes with nucleons (N-DURCA) and hyperons (Y-DURCA) are studied in the degenerate baryon matter of neutron stars. We investigate the effects of hyperon degrees of freedom and the Y-DURCA processes on the N-DURCA processes, and the total neutrino emissivity of neutron star matter. The results show that the existence of hyperons decreases the abundance of protons and leptons, and can sharply suppress the neutrino emissivity of the N-DURCA processes.