Graphene, a monolayer of carbon atoms arranged in a hexagonal pattern, provides a unique two-dimensional (2D) system exhibiting exotic phenomena such as quantum Hall effects, massless Dirac quasiparticle excitations and universal absorption & conductivity. The linear energy-momentum dispersion relation in graphene also offers the opportunity to mimic the physics of far-away relativistic particles like neutron stars and white dwarfs. In this letter, we perform a counterintuitive ultrafast pump-probe experiment with high photon energies to isolate the Drude-like intraband dynamics of photoexcited carriers. We directly demonstrate the relativistic nature of the photoexcited Dirac quasiparticles by observing a nonlinear scaling of the response with the density of photoexcited carriers. This is in striking contrast to the linear scaling that is usually observed in conventional materials. Our results also indicate strong electron-phonon coupling in graphene, leading to a sub-100 femtosecond thermalization between high energy photoexcited carriers and optical phonons.