You might be able to get away with this. I would use a hair dryer or something to make the tile limber and easy to bend. Then carefully pry up one corner and then carefully and slowly with a paint scraper, start lifting a small portion at a time. Heating as you go.
If you get it up, you will have to make sure that the new indended spot is clean, and free of all debris. I would first use a scraper like a wood chisel to remove the big stuff. Then possibly alcohol or small amounts of mineral spirits to break down the stuck stuff. Now if you get those two chemicals under the adjacent tiles, they will release or it will break down that glue.
Once clean, you need to re attach the tile you removed. I guess I would try possibly contact cement, maybe a small amount of vinyl tile adheasive. Contact cement will work, but you have no time for adjusting the tile, once its touched, its in place there.