Preheat the grill to medium-high. Heat oil in a medium saucepan on the grates of the grill or on a burner. Add the onion and cook until soft, about 3 minutes. Add the serrano chile and cook for 1 minute. Add the vinegar and sugar and cook until the sugar has melted. Stir in the chopped apples and cook until the apples are soft and the mixture is slightly thickened, about 10 minutes. Remove from the heat and let cool slightly. Place the apple mixture in a food processor and add the sage. Pulse until smooth. Season with salt and pepper, to taste. Let cool to room temperature.
Have a large drip pan filled with a little water positioned under where the turkey will be placed on the grill. Brush the entire turkey with oil and season with salt and pepper. Grill the turkey on all sides until golden brown. Reduce the heat of the grill to medium to maintain a constant temperature of 350 degrees F. Cook turkey until a thermometer inserted into the thigh registers 170 to 175 degrees F. Begin brushing the entire turkey with the apple glaze during the last 15 minutes of cooking. Remove from the grill and brush with more of the glaze. Let rest for 15 minutes before slicing. Grill the sliced apples for 2 to 3 minutes on each side and serve with the turkey.