Mirrors with excellent mechanical, thermal and optical properties are suitable for a broad spectrum of modern optical application. A growing number of multi- and hyperspectral imaging devices such as telescopes and spectrometers are based on all-reflective metal optics. Optics with higher mechanical or dynamic loads are often made of ceramics; at higher thermal loads, they are made of glass-ceramics. The DLR Earth Sensing Imaging Spectrometer (DESIS) is a space-based hyperspectral instrument developed by German Aerospace Center (DLR). The optical system of the spectrometer was designed, fabricated and pre-aligned by the Fraunhofer Institute of Applied Optics and Precision Engineering (IOF). The instrument was realized as an all-reflective system using metal-based mirrors using a modular, so-called snap-together approach. Parts of the system are flat mirrors for the pointing unit of the instrument. Two flat mirrors based on a metallic substrate material (Al 42Si) and one flat mirror based on a ceramic (HB Cesic®) were realized. The cost-efficient manufacturing technology of metal mirrors has an important advantage over glass, glass-ceramic and ceramic mirrors. For the pointing mirror, a more rigid and stiff material like HB-Cesic® was used. Different and tailored process chains were applied for both kinds of mirrors. The paper summarizes the fabrication of optical mirrors by i) grinding and polishing of ceramic matrix composite substrates; and ii) diamond machining combined with post-polishing techniques, like magnetorheological finishing (MRF) and chemical mechanical polishing (CMP) for metallic substrates. The process chains are described including testing setup and results with regard to different materials and manufacturing technologies. The mirrors show an excellent quality regarding flatness (lower 15 nm rms) and roughness (lower 1 nm rms, WLI magnification 50x).