Season the pork shoulder with ground cumin, dried oregano, sea salt, and black pepper, rubbing the spices thoroughly into the meat.
Place the seasoned pork in a slow cooker along with the orange juice, lime juice, smashed garlic cloves, and half of the white onion.
Cover and cook on low for 7 to 8 hours until the pork is tender and easily pulls apart with a fork.
Remove the pork from the slow cooker and shred it using two forks, discarding any excess fat while reserving a small amount of the cooking liquid.
Heat a non-stick skillet over medium-high heat and add the shredded pork, searing it until the edges become golden and crispy.
Warm the corn tortillas in a dry pan or over an open flame until they are soft and pliable.
Assemble the tacos by dividing the crispy pork between the tortillas and topping with the remaining white onion, sliced radishes, fresh cilantro, and salsa verde.