"Grund" most often means "reason".
But it can sometimes also mean "bottom" or "grounding" ("Er hat keinen Grund" could also mean, of someone who is swimming, "he is out of his depth; his feet do not touch the bottom of the lake/river/swimming pool").
But "ground" is usually "Boden"; "grounds" (as in the area around a house; or a fenced-in area for animals or the like) would be "Grundstück" or "Gelände". Or "Grundbesitz" if you think of it as something that you possess.
There is also "Untergrund" which can be underground or merely the basis holding up something.
kind of a non-issue, but where is the 'does' coming from? I know my translations a little off, but why doesn't it translate to 'he has no reason'- edit I was originally thinking reason as in rationality-? (I know you're not suppose to have a direct translation, still curious!)