How stem cells self-organize to form structured tissues is an unsolved problem. Intestinal organoids offer a model of self-organization as they generate stem cell zones (SCZs) of typical size even without a spatially structured environment. Here we examine processes governing the size of SCZs. We improve the viability and homogeneity of intestinal organoid cultures to enable long-term time-lapse imaging of multiple organoids in parallel. We find that SCZs are shaped by fission events under strong control of ion channel-mediated inflation and mechanosensitive Piezo-family channels. Fission occurs through stereotyped modes of dynamic behavior that differ in their coordination of budding and differentiation. Imaging and single-cell transcriptomics show that inflation drives acute stem cell differentiation and induces a stretch-responsive cell state characterized by large transcriptional changes, including upregulation of Piezo1. Our results reveal an intrinsic capacity of the intestinal epithelium to self-organize by modulating and then responding to its mechanical state.