spat = spit = to force out the contents of the mouth, especially saliva rudely = not polite; offensive grate = a metal structure which holds coal or wood in a fireplace

He spit (past tense) with great force and noise into the grate (metal or wood grating or lattice on the floor). To spit at all indoors is considered rude, but to do it with any noise is considered very rude. It is sometimes taken as an insult, but I doubt that is its purpose here.