Is there any way that I can remove these roots and let the driveway concrete slab (raised by the roots) settle to its original position?
I'm hesitant to say "no way" because if you spend enough time and money you could possibly get these out from below while supporting the slab and then somehow find a way to push it back down.
But I think that's going to be WAY more expensive than the usual solution which is to break up that section of the slab, remove the roots, fill and compact the area where they roots were, and finally pour a new section of slab.
Easiest is to just let the roots rot. You can tar or herbicide the ends (where you cut them) to keep them from sprouting. The slabs will hopefully settle back down to flat. It's possible they'll settle too much or crack, and then you can decide if you want to break them up. Otherwise you would just need to break them up now.