Can I use construction adhesive for backsplash tiles
I personally wouldn't cover up the existing tiles as the new ones will look twice as thick at the edges, and you'll have to match the old tiles exactly. It shouldn't be that hard to remove the old tiles. I would try using a metal putty knife and hammer. The putty knife should get right behind the tile and not do any real damage to the drywall behind. Then just do any surface repair with drywall compound. Then I would use a mastic or thinset depending on what type of tile you choose. I wouldn't use construction adhesive just because it literally will lock those tiles in place.