We propose a device to break the valley degeneracy in graphene and produce fully valley-polarized currents that can be either split or collimated to a high degree in a experimentally controllable way. The proposal combines two recent seminal ideas: negative refraction and the concept of valleytronics in graphene. The key new ingredient lies in the use of the specular shape of the Fermi surface of the two valleys when a high electronic density is induced by a gate voltage (trigonal warping). By changing the gate voltage in a n-p-n junction of a graphene transistor, the device can be used as a valley beam splitter, where each of the beams belong to a different valley, or as a collimator. The result is demonstrated through an optical analogy with two-dimensional photonic crystals.