Toss the carrots with the orange juice concentrate and refrigerate in a covered container for up to 8 hours. Bring a large pot of water to a boil over medium-high heat, add the linguine, and cook as directed on the package, until al dente. Drain.
Meanwhile, heat the oil in a large nonstick skillet over medium heat until hot but not smoking. Add the scallops and garlic and cook, stirring until the scallops are just opaque, about 3 minutes. Using a slotted spoon, transfer the scallops to a plate. Add the tomatoes, clam juice, salt and pepper to the skillet. Bring to a boil, stir in the carrots, reduce the heat, and simmer, stirring from time to time, until the sauce is thickened and slightly reduced, about 5 minutes.
Return the scallops to the skillet. Add the mint and cook until the scallops are warmed through, about 1 minute. Transfer the sauce to a large bowl, add the pasta, and toss. Divide among 4 bowls and serve.