The QCD axion, originally proposed to solve the strong CP problem in particle physics, is a viable dark matter candidate as well. If the Peccei-Quinn symmetry is broken after inflation, axion dark matter forms sub-planetary mass minihalos, which merge hierarchically into the larger dark matter halos of today. Recent proposals to test for the existence of these minihalos have motivated this work, which examines the dynamical effects that can disrupt minihalos. Analytic methods are used to investigate the effects of impulsive encounters with stars, and minihalo-minihalo interactions. Estimates of the energy imparted from these encounters are obtained, and survival times computed for various scenarios. Implications for microlensing caustics, pulsar timing arrays, and direct detection are discussed.