The existence of nonlinearity in a spintronic device is indispensable for spin-based complex signal-processing operations. Here we measure the presence of electron-spin-dependent nonlinearity in a van der Waals heterostructure spintronic device. We further demonstrate its application for basic analog operations such as essential elements of amplitude modulation and frequency sum (heterodyne detection) on pure spin signals, by exploiting the second-harmonic generation of the spin signal due to nonlinear spin injection. Furthermore, we show that the presence of nonlinearity in the spin signal has an amplifying effect on the energy-dependent conductivity-induced nonlinear spin-to-charge conversion effect. The interaction of the two spin-dependent nonlinear effects in the spin-transport channel leads to a highly efficient modulation of the spin-to-charge conversion effect, which in principle can also be measured without using a ferromagnetic detector. These effects are measured both at room and low temperatures, and are suitable for their applications as nonlinear circuit elements in the fields of advanced spintronics and spin-based neuromorphic computing.