Mechanical stretching of proteins modifies their folding kinetics and may also cause a switch of folding mechanism from that at zero force. It is not clear from the kinetics alone whether the change is a continuous distortion of the zero force pathway or it occurs via a "discrete switch" to an alternative pathway. We use molecular simulations to dissect this switch of mechanism as a pulling force is applied to protein G via four different pairs of residues, or "pulling coordinates". Using a statistical clustering approach based on the pattern of native contact formation, we find distinct unfolding mechanisms at low and high force. For pulling coordinates for which the protein is resistant to the applied force, a marked "turnover" in the force-dependent unfolding kinetics is associated with an abrupt switch to a novel mechanical unfolding pathway. In contrast, pulling along coordinates where the protein has low resistance to force induces a smoother acceleration in the unfolding rate and a more gradual shift in the unfolding mechanism. The switch in folding pathway is captured by projection onto appropriate two-dimensional free energy surfaces, which separate the low and high force transition states. Remarkably, we find for a weak coordinate that the high force transition state is already accessible in the absence of force. Brownian dynamics simulations on these surfaces capture the force dependence of the kinetics, supporting the use of simplified low-dimensional models for interpreting mechanical unfolding experiments. We discuss the implications of the switch in pathway for the mechanical strength of proteins, and how such a switch may be experimentally tested.