We introduce the notion of non-Abelian tensors and use them to construct a general non-Abelian time evolving block decimation (NA-TEBD) scheme that uses an arbitrary number of Abelian and non-Abelian symmetries. Our approach increases the speed and memory storage efficiency of matrix product state based computations by several orders of magnitude and makes large bond dimensions accessible even on simple desktop architectures. We use it to study post-quench dynamics in the repulsive SU(3) Hubbard model and to determine the time evolution of various local operators and correlation functions efficiently. Interactions turn algebraic charge relaxation into exponential and suppress coherent quantum oscillations rapidly.