Special equipment: 4 large bricks wrapped in aluminum foil and a pair of sharp kitchen shears
Combine the tangerine juice, lemon juice, canola oil, honey, coriander seeds, thyme and garlic in a large storage container. Whisk to combine.
Place 1 chicken, breast-side down, on a plastic cutting board and cut out the backbone with a pair of sharp kitchen shears. Reserve the backbone in a plastic storage bag and save for a later use (such as homemade chicken stock). Turn the chicken over and use your hands to gently press down on the breast to crack the breast bone so that it lays flat. Add the butterflied chicken to the container with the marinade. Repeat the process with the remaining chicken and nestle the birds side by side in the marinade, making sure that they are completely submerged. Cover with a lid and marinate in the refrigerator, flipping once halfway through, at least 8 hours and up to 24 hours.
Preheat an outdoor grill to medium-low to medium heat. While the grill heats up, remove the chickens from the marinade and pat fairly dry with paper towels. There should be a light coating of marinade on the chickens but not too much because excess oil will cause flare-ups on the grill. Discard the marinade. Season the chickens liberally on all sides with salt and pepper and tuck the wings under the breasts.
Place the chickens, breast-side down, on the hot grill and set 2 bricks on top of each chicken. Cook until the skin is light golden brown and crispy, about 25 minutes. Use tongs to carefully remove the bricks. Flip the chickens, return the bricks to the chickens and continue grilling until an instant-read thermometer inserted in to the thickest part of each chicken registers 165 degrees F, about 25 minutes more.
While the chicken is cooking, add the tangerines to the grill, cut-side down. Grill until the flesh is deeply charred in spots, about 10 minutes. Remove from the grill and cool slightly.
To serve, cut each chicken into 10 pieces and transfer them to a large platter. Nestle the grilled tangerines around the chicken pieces and top with the sprigs of mint. Serve immediately.