This is a form of coordination, where two different deletions are permitted. The underlying sentence is something like
We are bound by the laws, and we are not bound by the intent of our legislators.
(I'm not saying that anybody would say that; but that is the full logical form)
The repeated part can often be deleted in a coordination:
We are bound by the laws, and not by the intent of our legislators.
Finally, the coordinator and can often be dropped when it is directly followed by not. (Alternatively, you could regard not as a coordinator in its own right). This gives
We are bound by the laws, not by the intent of our legislators.
So the structure is that the second "by" clause is a parallel indirect object of the VP "We are bound".
As for the comma, I would regard it as optional in all of these; but I would put it in, because in speaking them I would take a new breath group for "not ... ". As far as I am concerned, most of the "rules" for using commas are arbitrary nonsense: the rule I prefer is "When you take a new breath group, write a comma or other punctuation".