Trim any excess thick fat from the pork shoulder and season all sides with 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 7-8 hours or on high for 4 hours until the meat is tender enough to be easily pulled apart.
Remove the pork from the slow cooker and shred it using two forks, discarding any large pieces of fat.
Heat a large non-stick skillet over medium-high heat and add the shredded pork in a single layer.
Press down with a spatula and cook for 3-4 minutes without moving until the bottom edges become crispy and golden brown.
Briefly warm the corn tortillas in a dry pan or over a gas flame until soft and slightly charred.
Divide the crispy pork between the tortillas and top with finely diced red onion, chopped cilantro, and thinly sliced radishes.