German groß means large, tall while English gross means… well.. something like disgusting.
So what happened?
Well, the English gross comes from an old Latin term that meant something like thick, coarse. From there it shifted a bit toward a more general sense of total which we can still see in phrasings like gross domestic product. It was also used as an intensifier, like for example grossly overstated or gross idiocy. And apparently, in the 1950s, students then started taking it as a slang term for something intensely bad.
And the German groß? Well, that one is actually related to great and while those too originally meant coarse, massive they don’t belong to the same family as gross, at least etymologically.