Cascading of collisionless trapped-electron mode turbulence via particle-induced scatterings is analytically investigated for axisymmetric tokamak plasmas. Our results demonstrate that the nonlinear mode-coupling processes depend crucially on both the parallel and radial mode structures associated with the realistic toroidal geometry. As a consequence, the scattering coefficients are found to be significantly suppressed with respect to those derived for slab-like models. For typical tokamak parameters, the wave energy cascades inversely towards lower toroidal mode numbers.