Grease a 6-quart slow cooker with non-stick cooking spray or insert a slow cooker liner.
In a medium bowl, mix graham cracker crumbs and melted butter until combined; press firmly into the bottom of the slow cooker to create a base.
In a large mixing bowl, whisk together chocolate cake mix, water, vegetable oil, and eggs until smooth.
Pour the cake batter over the graham cracker crust in the slow cooker.
Sprinkle the chocolate chips and 1 cup of the mini marshmallows over the top of the batter.
Cover and cook on HIGH for 2 to 2.5 hours (or LOW for 4 hours) until the cake is set and a toothpick comes out clean.
Remove the lid and sprinkle the remaining 1 cup of mini marshmallows and the broken graham cracker pieces over the top.
Replace the lid for 5 to 10 minutes until the marshmallows are softened and slightly melted.
Serve warm using a large spoon.