Low magnetic damping and high group velocity of spin waves (SWs) or magnons are two crucial parameters for functional magnonic devices. Magnonics research on signal processing and wave-based computation at GHz frequencies focused on the artificial ferrimagnetic garnet Y3Fe5O12 (YIG) so far. We report on spin wave spectroscopy studies performed on the natural mineral hematite (α-Fe2O3), which is a canted antiferromagnet. By means of broadband GHz spectroscopy and inelastic light scattering, we determine a damping coefficient of 1.1×10−5 and magnon group velocities of a few 10 km/s, respectively, at room temperature. Covering a large regime of wave vectors up to k ≈ 24 rad/μm, we find the exchange stiffness length to be relatively short and only about 1 Å. In a small magnetic field of 30 mT, the decay length of SWs is estimated to be 1.1 cm similar to the best YIG. Still, inelastic light scattering provides surprisingly broad and partly asymmetric resonance peaks. Their characteristic shape is induced by the large group velocities, low damping, and distribution of incident angles inside the laser beam. Our results promote hematite as an alternative and sustainable basis for magnonic devices with fast speeds and low losses based on a stable natural mineral.