Mix water, corn meal, mozzarella cheese, butter, and salt together in a large bowl. Knead until mixed well and the dough has a soft consistency. Form balls the size of a medium orange and place them between 2 sheets of plastic wrap. Flatten with a rolling pin to your desired thickness.
Cut the dough into circles using a cereal bowl or drinking glass, lip-down, through the plastic wrap. Remove the plastic wrap and remove excess dough.
Coat a griddle with cooking spray and heat to medium-high. Add arepas and grill until golden brown, about 5 minutes per side. Serve immediately.