I use the hoe to level out the ground first before placing the foundation no grass has ever grown up through the floor.
Consider leveling the ground may solve your problem as the foundation is off the ground.. Unless the mods are effecting it.

No. I have branches and mushrooms in my floor. I tried pulling the boards up and cultivating the ground but that did not help. I leveled before I built. Only thing you can do is make sure they are not there before you build, but if you find a great spot, your just going to have to deal with them.

If you lower the ground below your floor, the clutter spawn points should drop with it.

I'll need to lower my ground fairly well in order to hide them...
Advize's Plant Everything mod allows you to destroy (with no returns) many of the re-growing plantlife, but nothing for branches yet.