A central challenge in systems neuroscience is understanding how computational mechanisms-including those implemented within a single brain region-interact to produce behavior. For example, prior work in the literature attributes many computational functions to the cerebellum, but these functions have been tested in isolation and it remains unclear how they jointly contribute to motor control. Here, we test several established hypotheses of cerebellar function: internal modeling, timing of movement dynamics, sensory-error processing, delay processing, and multimodal integration. We first formalize these functions as mechanistic parameters within a computational model of speech motor control. We then use this formalism to investigate the relative contribution of each function to the abnormal speech corrective response seen in adults with cerebellar degeneration during perturbed auditory feedback. We find the following functions explain most of the behavioral differences: internal modeling, timing of movement dynamics, and multimodal integration. We also show that the key mechanisms have a trade-off relationship, and that cerebellar degeneration modulates those trade-off strengths and boundaries. These results both elaborate the mechanistic function of the cerebellum in speech feedback control and, more broadly, demonstrate the promise of using this paradigm to simultaneously test competing theories of neural function underlying behavior.