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We have performed time-resolved cyclotron resonance measurements in ultrapure diamond crystals for the temperature range of T=7.3–40 K and obtained the temperature-dependent momentum relaxation times based on the cyclotron resonance widths for optically generated electrons and holes. The relaxation time follows a T−3/2 law down to 12 K, which is expected for acoustic-phonon scattering without impurity effect because of the high purity of our samples. The deviation from the law at lower temperatures is explained by the impurity scattering and the breakdown of the high-temperature approximation for the phonon scattering. We extract the carrier drift mobility by using the directly measured effective masses and the relaxation times. The mobility at 10 K for 600 ns delay time after optical injection is found to be μe=1.5×106 cm2/V s for the electrons, and μlh=2.3×106 cm2/V s and  μhh=2.4×105 cm2/V s for the light and heavy holes, respectively. These high values are achieved by our high-sensitivity detection for low-density carriers (at <1011 cm−3) free from the carrier-carrier scattering as well as by the suppression of the impurity scattering in the high-purity samples.