Replacing a dishwasher and noticed they had tiled underneath and the dishwasher I purchased wouldn't fit. So I used an angle grinder and grout removel tool to remove the tiles down to the backer board and now the dishwasher fits. Yay! The ONLY issue left is that the granite countertop barely, and I mean barely scrapes up against the right corner of the dishwasher door. I feel like if I carefully grinded/sanded down the underside of the granite just a smidge, then the door would move freely. The only other option I can think of is to take the thing out, demo the backer board and subflooring, install new subflooring, and put the dishwasher directly on the subflooring, but that sounds like time or money I don't have, so leaning towards just grinding the granite a bit. Thoughts?
Sounds like the tile and backer board were put in after, and around the cabinets that were already in place? If so, then that's a common problem. Doing what you're suggesting makes it difficult to remove the dishwasher as you have to get it up over the lip of the tile floor.
I've done things two ways in the past to alleviate that sort of problem.
1) When doing a full kitchen demo or even just cabinet replacement, I've raised the cabinets up off the floor enough to compensate for the backer board+tile height. I ran the backer board under the cabinets, then put down a "frame" of 1/4"-1/2" plywood strips (the thickness of the tiles) that the cabinets would sit on. This way I didn't have to tile under the cabinets.
2) When just laying down a new floor (backer board+tile), I've removed and raised the counter top so that the dishwasher opening remained the same. In this case I was replacing the counter top anyway, so it wasn't much more work.