Cover any surfaces you need to protect with a drop sheet.
Then, pry the tiles off the floor by driving the bolster blade underneath them with your mallet. In this case we are starting with an exposed edge, so getting under the tiles is easy.
Use a heavy-duty floor scraper to take the bulk of the glue off the floor. As you get closer to any edges you want to protect, switch to a smaller paint scraper. That way you can control the length of your strokes more.
Continue until all the glue is off the floor.
To make the job easier, keep sweeping up as you go.