It's a heck of a lot easier to remove it all in one piece than it is to try to laboriously patch all the holes that removing it piecemeal would entail. (It also lets you more easily run the wires to your new undercabinet lights.) You can just replace it with a large single patch of either drywall or cement board, prime it, and be done and ready for the new backsplash on top of it.

lisa9774, Let me agree 110% with CircusPeanut I just finished doing this very same thing. Not for the reasons you want to do it but I decided if we are replacing 22+ feet of drywall on one side of a galley kitchen, I might as well repair the other side too. I popped off a few tiles to get a look at what they were adhered to. Then using a manual drywall saw I cut my first area so I could see inside to check for wires/plumbing pipe, etc. I then scored the top (up against the wall cabs) and then the bottom (against the counter top) with a brand new blade in a heavy-duty utility knife. I changed the blade often. Once those areas were scored it was rather easy to get the drywall saw in there and cut the drywall that didn't seperate with the utility knife scoring it. Replacing the drywall was easier than removing the old stuff, honest! Measure the area. I cut my drywall on the kitchen floor cement foundation, using a utility knife and a straight edge to score it really well. It should snap right at the score line and then you can cut through the last layer, the paper backing. Once you put the drywall up for size, double-measure for any outlets, openings, etc. Put the drywall back down and cut out those areas. Put in your drywall screws making sure to counter-sink them a bit so they don't poke out over the drywall mud. CircusPeanut was right on! I am pushing 60, heavy, with a couple disabiities that make it a bit difficult to stand or bend for too long and yet, I got that drywall up myself. You Can DO this and save the $$$ for something else!

I had to do this for my mom. The best thing I found was to take a hammer to the front of the tiles first. It wasn't necessarily hard enough to crack them, but it somehow made them fall off easier. Then you can use a very flat chisel and hammer behind the tile. One thing you don't want to do is to use a any type of curved bar (crow bar, claw?). I put that behind one tile to pry it away from the wall and the curved part went right into the wallboard. That was the only big repair we had to make. Her's had lath and cement underneath and there was still only minor damage to the rest. Have fun! I love demo!

I'm not a professional and it depends on the size of the area to be repaired, but it's pretty easy to cut out damaged dry wall and then mud the patch seams. You want to do whatever will maximize the clean, level surface. And, yes, you will need to feather and sand your mud until it is dead level. I wouldn't paint the mudded, repaired drywall before tiling, at least, I never have. And I've never primed drywall before mudding it. If you've only read or watched videos, be sure you practice. If your repair area is large, even if just 'paper', maybe hire somebody?