I have removed old ceramic flooring tiles from around my fireplace. I am putting down natural travertine all over the first floor, over a slab, and I am now planning on building a small ledge or step where the old fireplace tile used to be. My plan is to build a 3-inch-high shelf and then cover it with concrete backer board, and then put small tiles over that. My dilemma is, what shall I do with the old mortar that is left over from the removed tile? My attempts to chip away at it with a masonry chisel and hammer have take up not only mortar but also bits of the foundation, thus leaving a divot in the slab floor. Obviously I'm not pleased with that. Can I perhaps use a construction glue to glue my new shelf to the old mortar on the floor? Will it create a strong-enough bond? Also, a related question is, when I remove tile from the wall, it also creates a mess and peels off drywall. Shall I just cut out all of that drywall and mortar and put in new drywall, or perhaps just put backer board in where the drywall was, and tile over that?

You should consider building a form and pour a concrete slab where the fireplace hearth is to placed. Raise it to the height you want it to be. The fact that the floor in this area is roughed up is good. It will provide you with a better bond. To build it up with backerboard you would need six layers of 1/2" board to build it up the three inches you looking to have. Once the cement drys you will have a real good and strong support for what ever tile your going to place down for the hearth.
For around the fireplace simply cut out the rock and remove the old tiles then re-sheetrock it and replace with what ever tile your planning to use. Using Backer board is overkill and not needed in this application.

Thanks for the feedback. Is there any harm in building a low "shelf" to create the step up to the fireplace, in stead of pouring concrete? What if I used 2x4s to create a three-sided base, put plywood over that, and that backer board over that? Perhaps your suggestion of pouring concrete is more sound structurally, but if we want to make changes later, we will have a whole lot of concrete demo. to do. Does that make sense? Thanks again.

You cannot use any wood products for the hearth of a fireplace for safety reasons. You must consider when you would be changing the look of the fireplace and weigh it against taking it out later. It sounds like your spending a lot of money and time to redo the room and look, For the sake of a few bags of cement and to worry about taking it apart some time in the future is crazy. You would find anyway that the removal of the cement at a later date would be fairly easy. As its not going to bond that well anyway. Doing it with plywood etc will take a long time to build and because of the movement of wood as it drys out and moves becasue of humidity the tile on the backerboard most likely would crack or come loose.

Okay. You have sold me on the idea of pouring concrete. I will build a plywood form and buy a concrete mix that should give me a nice smooth surface upon which to tile. Thanks for the input.