Raman random fiber laser combined with passive sensing units can realize quasi-distributed sensing over ultra-long distances. However, limited by the spectrum detection speed, this sensing scheme is usually only applicable to static sensing fields. To address this issue, a novel Raman random fiber laser long-distance dynamic sensing system is proposed by integrating Raman random fiber laser with beat frequency interrogation. Firstly, the suitability of rapid spectral measurement for long-distance dynamic sensing is demonstrated based on the time-dependent spectrum-balanced model. Then, in the proof-of-concept experiment, the spectrum of Raman random fiber laser can be measured rapidly by processing the temporal signals of the local oscillator light and the random fiber laser after beating, breaking through the limitation of the round-trip time of the light on the sensing bandwidth. Meanwhile, the center wavelength of the spectrum is calibrated by using a denoising convolutional neural network, which significantly improves the signal quality of disturbance signal detection and achieves accurate measurement of disturbance information with different frequencies and waveforms. This research provides new insights for further expanding the application fields of Raman random fiber laser.