Next-generation high-brilliance X-ray photon sources call for new X-ray optics. Here we demonstrate the possibility of using monolithic diamond channel-cut crystals as high-heat-load beam-multiplexing 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 or 12.4 keV X-rays within a 15 meV bandwidth to ⁵⁷Fe or ⁴⁵Sc nuclear resonant scattering experiments, respectively. The crystal design allows out-of-band X-rays transmitted with minimal losses to alternative simultaneous experiments. Only ≲2% of the incident ∼100 W X-ray beam is absorbed in the 50 µm-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.