A variety of models of self-replicating processes have been proposed within the framework of two-dimensional cellular automata. They are heavily dependent on or limited by the peculiar properties of the lattice spaces. We introduced a new framework called graph automata to obtain a natural description of complicated spatio-temporal developmental processes such as self-replication. As an illustrative example, a self-replication of Turing machine is shown in a simple and straightforward formulation. Graph automata provide a new tool to approach important scientific problems such as evolution of morphology, and also to give the basis of self-replicating and self-repairing artifacts.