Next-generation, high-brilliance x-ray photon sources call for new x-ray optics. Here we demonstrate the feasibility of using monolithic diamond channel-cut crystals as high-heat-load, beammultiplexing, narrow-band, mechanically-stable x-ray monochromators with high-power x-ray beams at cutting-edge, high-repetition-rate x-ray free-electron laser (XFEL) facilities. The diamond channel-cut crystals fabricated and characterized in these studies are designed as two-bounce Bragg reflection monochromators directing 14.4-keV or 12.4-keV x-rays within a 15-meV-bandwidth to 57 Fe or 45 Sc nuclear resonant scattering experiments, respectively. The crystal design allows out-ofband x-rays within a 1-eV XFEL bandwidth to be transmitted with minimal losses to alternative simultaneous experiments. Only 2% of the incident 100-W x-ray beam is absorbed in a 50µm-thick first diamond crystal reflector, ensuring that the monochromator crystal is highly stable. Other x-ray optics applications of diamond channel-cut crystals are anticipated.