Preheat oven to 375°F. Drain mandarin oranges and reserve juice. Zest limes, cut in half and juice. Stem and coarsely chop mint. Peel shallot and thinly slice. Pat pork chops dry and season both sides with half the lime zest and a pinch of pepper.
Place reserved mandarin orange juice, half the lime juice, all of the olive oil except for what is needed for the pan to cook the pork chops, honey, mint (reserve a pinch for garnish), remaining lime zest and a pinch of pepper in a large mixing bowl. Mix thoroughly; set aside 1 tablespoon dressing for each pork chop.
Heat 1-2 teaspoon olive oil in a pan over medium heat. Place pork chops in pan and cook until golden brown, 2-3 minutes per side. Transfer pork chops to prepared baking sheet. Pork chops will finish cooking in a later step.
Place baking sheet in oven and roast until pork chops reach a minimum internal temperature of 145°F, 8-10 minutes. Rest 5 minutes. While pork chops rest, make salad.
Stir dressing to recombine. Add arugula, mandarin oranges and shallots (to taste) to dressing. Toss to coat. Plate dish as pictured, topping pork chops with remaining dressing. Garnish salad with slivered almonds and remaining mint. Bon appétit!