Nonlinear phenomena in the THz spectral domain are important for understanding the optoelectronic properties of quantum systems and provide a basis for modern information technologies. Here, we report a giant THz nonlinearity in high-mobility 2D topological insulators based on HgTe quantum wells, which manifests itself in a highly efficient third harmonic generation. We observe a third harmonic THz susceptibility several times higher than that in bare graphene and many orders of magnitude higher than that in trivial quantum well structures based on other materials. To explain the strong nonlinearity of HgTe-based heterostructures at the THz frequencies, we consider the acceleration of free carriers with a high mobility and variable dispersion. This acceleration model, for which the nonparabolicity of the band dispersion is key, in combination with independently measured scattering time and conductivity, is in good agreement with our experimental data in a wide temperature range for THz fields below the saturation. Our approach provides a route to material engineering for THz applications based on frequency conversion.