Make the masa by using a hand grater to grate the yautia and unripe plantains using the finest texture. Place all of the grated ingredients in a large bowl. Add the olive oil and salt and stir to combine well. Cover and refrigerate for 30 minutes or overnight.
To make the picadillo, heat 1 tablespoon of vegetable oil in an 8-inch skillet. Saute the onion and bell pepper for 2 minutes, and then add the ground meat and garlic. Brown the meat until it is well cooked, about 10 minutes. Add the olives and capers and season with salt and pepper. Remove from the heat.
Heat the vegetable oil for frying to between 350F and 375F in a 10-inch skillet. Preheat the oven to the lowest setting to keep the fried fritters warm.
Cut an 8-inch-by-10-inch piece of aluminum foil. Spray one side with vegetable spray. Using a 1/4 cup measuring cup, scoop the refrigerated masa mixture onto the oiled surface of the foil. Using a spoon, flatten out the masa into a circle. Place 2 teaspoons of the picadillo mixture in the middle of the masa. Fold the foil over so that the masa makes a pocket shape encasing the picadillo. Shape the alcapurria outside the foil so that it is oval shaped. The foil should remove easily from the alcapurria.
Place the alcapurria carefully in the hot oil, and fry for about 3 minutes on each side, until it is golden brown. Drain on paper towels, and keep warm in the oven until all of the alcapurrias are prepared.