Your description is a little unclear. Are you saying that the whole house is on a slab and that the brick hearth may be supported by a small slab on top of the main slab? If so, there seem to be two possibilities here:

1. If the smaller slab was poured on top of the main slab after the first slab had cured, this would be the less difficult situation as the pieces of the top slab might separate from the one under it as you demo'ed. This would leave a relatively flat surface to deal with.

2. If the raised portion of the slab underneath the brick was poured at the same time as the main slab was, demo'ing that part of the concrete would take a lot of work, and then there would be a lot of work to level the rough surface.

Whichever situation it is, the approach would be to isolate the work area with floor-to ceiling-visqueen, remove the brick with a hand sledge and chisel, rent a concrete-cutting power saw with a diamond blade, and make parallel cuts several inches apart across the slab you want to get rid of. Then you would use a sledge and chisel and work from the side to break off pieces of concrete that rose above floor level to incrementally remove the whole thing. And of course you would wear a high quality respirator (not a dust mask) and a face shield while doing this. If the floor surface was rough when you finished, you would need to level it with a handheld grinder with a diamond cup, and this would raise further clouds of dust.

So, the bottom line is that it can be done, but involves a bit of work and a lot of mess.

Do you have any photos you can post to show what you are actually dealing with?