To overcome the challenge of using two-dimensional materials for nanoelectronic devices, we propose two-dimensional topological insulator field-effect transistors that switch based on the modulation of scattering. We model transistors made of two-dimensional topological insulator ribbons accounting for scattering with phonons and imperfections. In the on-state, the Fermi level lies in the bulk bandgap and the electrons travel ballistically through the topologically protected edge states even in the presence of imperfections. In the off-state the Fermi level moves into the bandgap and electrons suffer from severe back-scattering. An off-current more than two-orders below the on-current is demonstrated and a high on-current is maintained even in the presence of imperfections. At low drain-source bias, the output characteristics are like those of conventional field-effect transistors, at large drain-source bias negative differential resistance is revealed. Complementary n- and p-type devices can be made enabling high-performance and low-power electronic circuits using imperfect two-dimensional topological insulators.