Using a Solvent
Apply mineral spirits to a clean cloth or rag. Place the cloth or rag over the glue or caulking and let it set for at least four hours. This will allow the glue to soften.
Take the cloth or rag off of the old glue or caulk and then use another clean cloth to remove it from the cabinets. Run the cloth over the glue to wipe it off of the cabinet.
Apply additional mineral spirits to a cloth or rag and place it on the remaining cabinets to remove the glue. Wipe the glue off with a fresh cloth.
Scraping and Sanding
Run a utility knife along the edge of the caulking to cut it.
Pull of any loose caulking off with your hands. Use a pair of needle nosed pliers if your hands are to too big to grab the caulking.
Scrape the caulking with a metal scraper or putty knife to remove the old caulking from the kitchen cabinets.
Plug in a hand sander into an electrical outlet and then run it over the glue or caulk to sand it away. If you do not have a hand sander you can use pieces of sandpaper and rub it by hand. Repeat this process to remove any stubborn kitchen cabinet glue.