Most likely those are carriage bolts - a square section of the bolt shank engages to a square hole in what's left of the handle. However the carriage bolt's ability to resist turning is quite limited. Once it cams out (rounds out the square hole), any hopes of unscrewing it non-destructively are dashed. Pencil a line across handle and bolt so you can see when it's spun; if it turns more than 45 degrees it's a goner.
Grinding off the button-head outside will not help you. The square bolt shank will not pull through to the inside.
Don't be bashful about wrecking the inside handle, those are stock handles at a garage door supply house, I just mail-order them. Don't wreck the door (or more precise, its protective coating, why is it not rusting?)
I would start by sawing off any excess length of machine screw, the better to not have to remove rust from it. Trying to run a nut up over crumbly rust is trying to fail. Then hose the nut down with some proper penetrating oil like Kroil.
Then give it a shot with a wrench but use a socket wrench preferably 6-point so you don't round over the nut hexes. The outer half-handle will want to turn, hold it so it doesn't gouge the door finish. Once the carriage bolt head starts turning against the door handle remains, it has cammed out and you are done.
Now you're going to have to saw the nut off with a Dremel or better, a vibrating tool.