Using a first-principles-based effective Hamiltonian within molecular dynamics simulations, we discover that applying an electric field that is opposite to the initial direction of the polarization results in a switching of both the polarization and the magnetic chirality vector of multiferroic BiFeO3 at an ultrafast pace (namely, of the order of picoseconds). We discuss the origin of such a double ultrafast switching, which is found to involve original intermediate magnetic states and may hold promise for designing various devices.