Understanding magnetoresistance, the change in electrical resistance under an external magnetic field, at the atomic level is of great interest both fundamentally and technologically. Graphene and other two-dimensional layered materials provide an unprecedented opportunity to explore magnetoresistance at its nascent stage of structural formation. Here we report an extremely large local magnetoresistance of ∼2,000% at 400 K and a non-local magnetoresistance of >90,000% in an applied magnetic field of 9 T at 300 K in few-layer graphene/boron-nitride heterostructures. The local magnetoresistance is understood to arise from large differential transport parameters, such as the carrier mobility, across various layers of few-layer graphene upon a normal magnetic field, whereas the non-local magnetoresistance is due to the magnetic field induced Ettingshausen-Nernst effect. Non-local magnetoresistance suggests the possibility of a graphene-based gate tunable thermal switch. In addition, our results demonstrate that graphene heterostructures may be promising for magnetic field sensing applications.