Remove your cabinets from your walls. You'll need to unscrew any brackets, braces or clips that are securing them. Put them safely to one side if you intend to put them back up.
Put on a pair of gloves and apply a heat gun on a medium setting to an area of laminate backsplash. This will soften the adhesive that's securing it to your wall. If you don't soften the glue, you risk chipping away plaster from your walls when you remove the backsplash.
Position a scraper in between a join on your laminate backsplash where you've just applied heat and knock the top of its handle with a hammer. If you can't find a join, use a hammer and chisel to make a break in your backsplash.
Apply heat to the rest of your backsplash gradually and use the hammer and scraper to pry it from the wall.
Heat any glue residue left on your walls with the heat gun and use the scraper to remove it.
Wipe over your walls with warm water and detergent.