You can try using goo-gone to soften the glue.
If its liquid type glue ,its made to soak into the wood and bond the fibers. That can't be separated without damage. If its a gel or caulk type glue, it creates a bond between the two pieces. You may be able to cut into the glue with a sharp putty knife. My opinion its not worth the effort. There will always be some damage.
How do I get it between the boards?
Start with the putty knife at a corner and move it side to side while pushing to cut into the glue. Keep your hands a safe distance away or use clamps to secure it to a table/workbench.
Try using fishing line like dental floss and just saw between the two pieces.
Try a heat gun or hair dryer. Heat on the back side and gently pry apart.