We demonstrate that single layer graphene exhibits a strong nonlinear photon-mixing effect in the terahertz frequency regime. Up to room temperature, the third-order nonlinear current in graphene grows rapidly with increasing temperature. The third-order nonlinear current can be as strong as the linear current under a moderate electric field strength of ${10}^4\mathrm{V}/\mathrm{cm}$. Because of the unique Dirac behavior of the graphene quasi-particles, low Fermi level and electron fillings optimizes the optical nonlinearity. Under a strong-field condition, the strong-field-induced Dirac fermion population redistribution and nonequilibrium carrier heating effects further amplify the optical nonlinearity of graphene. Our results suggest that doped graphene can potentially be utilized as a strong terahertz photon mixer in the room-temperature regime.