Stir together brown sugar, soy sauce, 2 tablespoons water, Worcestershire sauce, cornstarch, and fish sauce in a small bowl. Set aside.
Using a meat mallet or the back of a knife, carefully crack the crab claws, removing any stray pieces of shell and ensuring the meat inside is easily accessible.
Heat oil in a large skillet over medium. Add lime wedges; cook 3 minutes. Add ginger, chile, and garlic; cook, stirring often, about 2 minutes. Add crab claws; toss to coat.
Add brown sugar mixture to skillet; stir to coat. Cook over medium, stirring occasionally, until sauce thickens, about 1 minute.
Remove from heat; sprinkle with mint and cilantro. Serve immediately.