AFAIK, there is no easy way to do this based on group membership. That is because the security model actually uses user permissions (a group is a container for multiple permissions with associated users). There is no permission defined for signature or no signature.
If you don't care about controlling this at the group level, you can manually remove the signature setting options from the profile form in the template. (and the post options if you wan to hide it even more). This will "turn it off" for all users because they can't set it.