Graphene is a nonlinear material in the terahertz (THz) frequency range, with χ(3) ∼ 10-9 m2/V2 ∼ 15 orders of magnitude higher than that of other materials used in the THz range, such as GaAs or lithium niobate. This nonlinear behavior, combined with ultrafast dynamic for excited carriers, proved to be essential for third harmonic generation in the sub-THz and low (<2.5 THz) THz range, using moderate (60 kV/cm) fields and at room temperature. Here, we show that, for monochromatic high peak power (1.8 W) input THz signals, emitted by a quantum cascade laser, the nonlinearity can be controlled using an ionic liquid gate that tunes the graphene Fermi energy up to >1.2 eV. Pump and probe experiments reveal an intense absorption nonlinearity at 3.2 THz, with a dominant 3rd-order contribution at EF > 0.7 eV, hence opening intriguing perspectives per engineering novel architectures for light generation at frequencies > 9 THz.