Axolotls are unique in their ability to regenerate the spinal cord. However, the mechanisms that underlie this phenomenon remain poorly understood. Previously, we showed that resting stem cells in the axolotl spinal cord revert to a molecular state resembling embryonic neuroepithelial cells and functionally acquire rapid proliferative divisions during regeneration. Here we refine in space and time this increase in cell proliferation during regeneration, and identify a dynamic high-proliferation zone in the regenerating spinal cord. By tracking sparsely-labeled cells, we quantify cell influx into the regenerate. Taking a mathematical modelling approach, we integrate these quantitative biological datasets across cellular and tissue level to provide a mechanistic and quantitative understanding of regenerative spinal cord outgrowth. We find that the acceleration of the cell cycle is necessary and sufficient to drive the outgrowth of the regenerating spinal cord in axolotls.