In a large bowl, whisk together 1/2 cup of the cider, the apple cider vinegar, oil, shallots, salt, black pepper and half of the sage. Add the pork loin, cover and set aside to marinade.
Set up a grill and set it for medium heat, ranging from 350-425 degrees F. When the grill is hot, take the pork out of the marinade, (reserve the marinade) place on the grill, turning occasionally. Stick with an instant read thermometer inserted in the center of meat reads 150 degrees F. This should take about 20 minutes total. Transfer to a cutting board and place foil over the loin like a tent and allow the loin to rest.
While the loin is resting, pour the marinade in a small saucepan and add the remaining apple cider, and 1/3 cup cinnamon applesauce, bring to a boil. Reduce heat and simmer until liquid is reduced in half, this could take 5-8 minutes. During the last minute whisk in the butter.
Slice the pork tenderloin into 3/8″ slices, place on plates and drizzle with the sauce and sprinkle with the rest of the chopped sage.