Preheat the grill to around 350°F (177° C).
Add the cream cheese to a large mixing bowl and beat with a hand mixer until smooth.
Add the buffalo sauce and ranch dressing to the cream cheese and mix until well combined.
Add the chicken and grated mozzarella cheese to the bowl and stir until all of the ingredients are well incorporated.
Pour the mixture into a 10" cast iron skillet and spread around into an even layer. Place on the grill over indirect heat. Stir every 10 minutes or so until it's heated through and the cream cheese is completely melted.
Once it's heated through and the cream cheese is completely melted, remove from the heat. Top with additonal buffalo sauce, blue cheese, and green onions if desired. Let cool slightly before serving.