I am unsure as to keeping the enemy from working a certain tile also keeps him from getting access to that recourse but I believe it does.
As an alternative you can also pillage the road in that spot. Even if it does not destroy an improvement you cannot see it does destroy the route and therefore acces to the recourse.
According to DanF, IIRC sitting on the enemy mine, while disallowing them to work the tile, does not remove their access to it, so you'd best pillage it.
Also, even if you can't see the resource I think you can still pillage the improvement first (in fact you must) before the road, right?