If you can actually get it off the doors, it will be so badly damaged from trying to remove it you won't be able to apply it to the floor.
And don't worry about the couple of extra pounds worth of Dynamat in the doors. It's not enough weight to effect the car in performance or economy.
I'd just leave it on if I were you. I tried to pull some off on my truck once so I could move it over a bit. Not only was it a pain to get any of it off, but it also took the paint right off of the metal with it and left it bare metal.

And I really doubt you'll want any of your paint pulled off your Mazda 3.
Do yourself a big favor and leave the stuff on the doors and don't worry about it...