Debris disks are scaled-up analogs of the Kuiper Belt in which dust is generated by collisions between planetesimals. In the collisional cascade model of debris disks, the dust lost to radiation pressure and winds is constantly replenished by grinding collisions between planetesimals. The model assumes that collisions are destructive and involve large velocities; this assumption has not been tested beyond our solar system. We present 0.'' 25 (approximate to 2.4 au) resolution observations of the lambda = 450 mu m dust continuum emission from the debris disk around the nearby M dwarf AU Microscopii with the Atacama Large Millimeter/submillimeter Array. We use parametric models to describe the disk structure, and a Monte Carlo Markov Chain (MCMC) algorithm to explore the posterior distributions of the model parameters; we fit the structure of the disk to both our data and archival lambda = 1.3 mm data (Daley et al. 2019), from which we obtain two aspect ratio measurements at 1.3 mm (h(1300) = 0.025(-0.002)(+0.008)) and at 450 mu m (h(450) = 0.019(-0.001)(+0.006)), as well as the grain-size distribution index q = 3.03 +/- 0.02. Contextualizing our aspect ratio measurements within the modeling framework laid out in Pan & Schlichting (2012), we derive a power-law index of velocity dispersion as a function of grain size p = 0.28 +/- 0.06 for the AU Mic debris disk. This result implies that smaller bodies are more easily disrupted than larger bodies by collisions, which is inconsistent with the strength regime usually assumed for such small bodies. Possible explanations for this discrepancy are discussed.