Prepare a grill for medium heat (350 to 450; you can hold your hand 5 in. above cooking grate only 5 to 7 seconds).
Whisk together 1/2 cup cider, the vinegar, oil, shallot, salt, and 1 tbsp. sage in a large bowl.
Add pork pieces to bowl and set aside.
When grill is hot, remove pork, reserving marinade, and cook, turning occasionally, until an instant-read thermometer inserted in center of meat reads 150, about 20 minutes total.
Transfer to a cutting board and tent with foil to rest.
Meanwhile, in a small saucepan, bring marinade and remaining 1/2 cup cider to a boil. Reduce heat and simmer until liquid is reduced by half, 6 to 7 minutes. During last minute, whisk in butter.
Cut pork into 1/4-in. slices, drizzle portions with sauce, and sprinkle with remaining sage.
