You are describing an early mud-job floor with dropped sheathing. The floor boards sit on strips of wood nailed to the sides of the joists and are below the tops of the joists, allowing for a very thick bed of mortar. Inexplicably, the tops of the joists were sawn to a point. which is why the mud bed (and tiles) usually crack along each joist. You have to access the plumbing through the ceiling below. If the pipes are actually corroded in the mortar, then they would have to be cut and dropped out. Any damage to the tile would be limited to an area hidden by a pipe escutcheon.
Casey

Casey, Thanks for the response. Our plumber spent several hours cutting into the ceiling below the problem, including up through what appeared to be a false floor, and could never find any pipes except for the tub drain. He seems to think he's going to have to remove the tub and access the plumbing that way. He's not a young kid plumber and seems to be giving this a lot of thought.

It is likely easier to simply disconnect the old drain and install a new one, possibly using a different route.

Someyimes there is enough room among the sloped boards and the ceiling below to rn a new line.
If it is tight you may have to use copper DWV since it has a smaller OD than plastic of the same size.

It is NOT worth tearing into a thick mud bed to repair an embedded pipe.