Purée garlic, ginger, sake, gochujang, mirin, and ¼ cup oil in a blender. Set ¼ cup marinade aside; chill. Transfer remaining marinade to a large dish. Add pork; turn to coat. Chill, turning occasionally, at least 2 hours.

Prepare grill for medium-high heat; oil grate. Remove pork from marinade and grill, basting with reserved marinade, turning occasionally, and moving pork to a cooler area if flare-up occurs, until cooked to desired doneness, 8–10 minutes for medium-rare.

Transfer pork to a cutting board and let rest 5 minutes before thinly slicing against the grain.