Grid homology is a combinatorial reconstruction of the knot Floer homology. There is an extention of grid homology for transverse spatial graphs, which is known to be related to sutured Floer homology. In this talk, I will show that if a spatial graph has a sink, source, or cut edge, then its grid homology is trivial. As an application, I will give a purely combinatorial proof of a K ̈unneth formula for the knot Floer homology of connected sums in the framework of the grid homology.