Trim excess fat from the pork shoulder and cut into large chunks.
Season the pork chunks evenly with the ground cumin, dried oregano, sea salt, and black pepper.
Place the seasoned pork into a slow cooker and add the minced garlic, orange juice, and lime juice.
Cover and cook on low for 7 to 8 hours until the meat is tender enough to pull apart easily with a fork.
Remove the pork from the slow cooker, shred it with two forks, and spread it on a baking sheet.
Broil the shredded pork for 3 to 5 minutes until the edges are golden and crispy.
Warm the corn tortillas in a dry skillet over medium heat for 30 seconds per side.
Fill each tortilla with a generous portion of the crispy pork and top with diced red onion, fresh cilantro, and sliced radishes.