The only solution that would be feasible to me is using a "Fein Tool", which is a high-speed vibrating saw tool. You can put in a flush-cut saw blade, lay a piece of 1/2" or so plywood on the floor (to protect the floor AND give a nice cut to the door bottom) then lay the tool flush down and cut off the bottom of the door.
My tool originally cost me $300.00, but Harbor Freight has a knock-off for $40.00. And these have gotten some good reviews... Looks like they give you enough blades to do this task in the new package.
Even if it is used only for this job, it will save you a whole lot of money and time vs. tearing the wall out, as was suggested.
The "difficult part" of this job seems to be that these saw blades are very slender, and so you might have to make slices several times in order to get enough clearance to pull the waste out from the bottom of the door.... So you make a cut(s), then tear out a few inches of the waste, then slide the door closed as far as you can, and cut some more.
One more thing is the blades DO NOT like cutting anything other than wood, so no hardware or nails or stone or tile. If you treat the blade nicely it will last a long time.
You should be able to do this thing in less than an hour. Or so. Good Luck.