What you want is a tilemap and NOT a tiled background. A tiled background is 1 image that you "stretch" over your whole layout to use it as a static background (ok, it can scroll, but i don't want make it more complicated here).
For the beginning save your tiles (rock, stone..whatever) in a 2-d Array and draw it on screen. When one tile gets destroyed you change it in the array.
For example, you say 1 is rock:
then one rock breaks (2 is broken rock):