Tear Down was the original demolition tool that players were given in alpha releases. Marking a tile for Tear Down will cause Builders to only demolish the wall on top of a floor, rather than the floor itself, as opposed to vaporizing the tile.
This is a very useful tool when constructing additional hallways or expanding rooms. First, draw the new dimensions of the room you want and let your Builders build it. Second, mark the dividing wall between the two sections (the new section and the old section) for Tear Down. You will then have a bigger room or hallway without exposing the old room to vacuum.