Bring potatoes, water, and beer to a boil in a large saucepan over high heat. Reduce heat to medium-low, cover, and simmer 5 minutes. Stir in the sausage, green onions, salt, black pepper, cayenne pepper, mustard powder, and liquid smoke. Cover and simmer until the potatoes are completely tender, about 15 minutes. When the potatoes are tender, stir in the Cheddar cheese until completely melted, then add the milk. Heat through, stirring until cheese has melted but do not boil.