We present high-reflectivity substrate-transferred single-crystal GaAs/AlGaAs interference coatings at a center wavelength of 4.54 μm with record-low excess optical loss below 10 parts per million. These high-performance mirrors are realized via a novel microfabrication process that differs significantly from the production of amorphous multilayers generated via physical vapor deposition processes. This new process enables reduced scatter loss due to the low surface and interfacial roughness, while low background doping in epitaxial growth ensures strongly reduced absorption. We report on a suite of optical measurements, including cavity ring-down, transmittance spectroscopy, and direct absorption tests to reveal the optical losses for a set of prototype mirrors. In the course of these measurements, we observe a unique polarization-orientation-dependent loss mechanism which we attribute to elastic anisotropy of these strained epitaxial multilayers. A future increase in layer count and a corresponding reduction of transmittance will enable optical resonators with a finesse in excess of 100 000 in the mid-infrared spectral region, allowing for advances in high resolution spectroscopy, narrow-linewidth laser stabilization, and ultrasensitive measurements of various light-matter interactions.