Combine the mango, red onion, cilantro, lime juice, 1/4 teaspoon salt and a few grinds of pepper in a medium bowl; set aside.
Heat the vegetable oil in a large nonstick skillet over medium-high heat. Add the ground beef and cook, stirring occasionally, until it starts browning, about 2 minutes. Stir in the tomatoes, chile powder and 3/4 teaspoon salt. Continue to cook until the beef is cooked through and the sauce is slightly reduced, about 2 minutes.
Divide the beef among the tostadas; top with lettuce, the mango salsa, sour cream and cilantro. Sprinkle with chile powder, if desired. Serve with lime wedges.