Debris disks are scaled-up analogs of the Kuiper Belt in which dust is generated by collisions between planetesimals. A foundation of our understanding of debris disks is the concept of a “collisional cascade,” where the mass loss from radiation pressure within a disk is replenished by larger planetesimals colliding with smaller bodies. One standard assumption of this model is that the collisions are destructive and involve large velocities, but this assumption has not been tested outside of the Solar System. We present 0.25” resolution observations of the λ = 450 μm dust continuum emission from the debris disk around the nearby M dwarf AU Microscopii with the Atacama Large Millimeter/submillimeter Array. We use parametric MCMC models to fit the structure of the disk, including the scale height, from which we derive the velocity dispersion. We compare our results with existing measurements of the disk scale height at λ = 1.3 mm (Daley et al. 2019), which allows us to derive the power-law slope of the grain-size dependent velocity dispersion. Interpreting our results within the modeling framework laid out in Pan & Schlichting (2012), we infer erosive rather than destructive collisions between grains within the AU Mic debris disk.