To establish and maintain organ structure and function, tissues need to balance stem cell proliferation and differentiation rates and coordinate cell fate with position. By quantifying and modelling tissue stress and deformation in the mammalian epidermis, we find that this balance is coordinated through local mechanical forces generated by cell division and delamination. Proliferation within the basal stem/progenitor layer, which displays features of a jammed, solid-like state, leads to crowding, thereby locally distorting cell shape and stress distribution. The resulting decrease in cortical tension and increased cell-cell adhesion trigger differentiation and subsequent delamination, reinstating basal cell layer density. After delamination, cells establish a high-tension state as they increase myosin II activity and convert to E-cadherin-dominated adhesion, thereby reinforcing the boundary between basal and suprabasal layers. Our results uncover how biomechanical signalling integrates single-cell behaviours to couple proliferation, cell fate and positioning to generate a multilayered tissue.