Asexual freshwater planarians reproduce by transverse bisection (binary fission) into two pieces. This process produces a head and a tail, which fully regenerate within 1-2 weeks. How planarians split into two offspring -using only their musculature and substrate traction -is a challenging biomechanics problem. We found that three different species, Dugesia japonica, Girardia tigrina and Schmidtea mediterranea, have evolved three different mechanical solutions to self-bisect. Using time lapse imaging of the fission process, we quantitatively characterize the main steps of division in the three species and extract the distinct and shared key features. Across the three species, planarians actively alter their body shape, regulate substrate traction, and use their muscles to generate tensile stresses large enough to overcome the ultimate tensile strength of the tissue. Moreover, we show that how each planarian species divides dictates how resources are split among its offspring. This ultimately determines offspring survival and reproductive success. Thus, heterospecific differences in the mechanics of self-bisection of individual worms explain the observed differences in the population reproductive strategies of different planarian species.