Break any caulk lines that exist between the laminate backsplash and other areas like the countertop. Use a utility knife to break the caulk line.
Apply heat to the laminate backsplash with a heat gun. Applying heat to the backsplash with the heat gun will soften the glue.
Slide a large putty knife between the laminate backsplash and the oak cabinet. Work carefully so you do not damage the wood on the cabinet. Move the putty knife back and forth until the laminate can be completely removed from the cabinet.
Remove the glue from the oak cabinet. There will be glue residue left on the surface of the cabinet. Allow the glue to cool down from the heat gun. Apply the adhesive remover with a paintbrush. Let the adhesive remover sit on the glue as long as the manufacturer directions recommend. Remove the adhesive remover with a putty knife and rag.