Concrete cutting or a whole new slab
If one corner of a driveway or patio has cracked or sunk and the rest is sound, cutting that section out along clean lines and pouring new is usually the better buy. Sometimes the cracking runs across the whole slab, or the base under it has settled. The base is what the slab sits on. In that case I'll tell you plainly that a new concrete driveway or a new concrete patio is the honest answer, because a patch on bad ground tends to crack along the old lines.
What shapes the cost of concrete cutting
A cut through a wall usually costs more than a cut across a slab, because the track saw has to be set up on its rail first. Some things add time. That includes thick concrete that needs more than one pass, and rebar, the steel set inside to hold it together. Long runs of cut and tight spots the saw can't reach easily add time too. Cleanup counts as well, so the plan for the slurry, the wet waste from cutting, and for hauling broken pieces away both show up in the price.