Avalanches and other hazardous mass movements pose a danger to the population and critical infrastructure in alpine areas. Hence, understanding and continuously monitoring mass movements are crucial to mitigate their risk. We propose to use Distributed Acoustic Sensing (DAS) to measure strain rate along a fiber-optic cable to characterize ground deformation induced by avalanches. We recorded 12 snow avalanches of various dimensions at the Vallée de la Sionne test site in Switzerland, utilizing existing fiber-optic infrastructure and a DAS interrogation unit during the winter 2020/2021. By training a Bayesian Gaussian Mixture Model, we automatically characterize and classify avalanche-induced ground deformations using physical properties extracted from the frequency-wavenumber and frequency-velocity domain of the DAS recordings. The resulting model can estimate the probability of avalanches in the DAS data and is able to differentiate between the avalanche-generated seismic near-field, the seismo-acoustic far-field, and the mass movement propagating on top of the fiber. By analyzing the mass-movement propagation signals, we are able to identify group velocity packages within an avalanche that propagate faster than the phase velocity of the avalanche front, indicating complex internal structures. Importantly, we show that the seismo-acoustic far-field can be detected before the avalanche reaches the fiber-optic array, highlighting DAS as a potential research and early warning tool for hazardous mass movements.