All our organs are lined with a protective epithelial layer essential to organ function. Yet, epithelial cells turn over via cell death and cell division at the highest rates in the body. If there are too few cells, the barrier is at risk; with too many cells, tumors can form. How are these two processes linked to maintain constant cell densities? We found that mechanical forces control both processes: cell stretching triggers rapid cell division, whereas crowding causes cell death by a process we call epithelial extrusion, in which cells fated to die are seamlessly squeezed out from epithelia.