Combine whole-wheat flour, all-purpose flour, cumin, salt and cayenne in a medium bowl. Whisk in beer to create a batter.
Coat half the tilapia pieces in the batter. Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Letting excess batter drip back into the bowl, add the fish to the pan; cook until crispy and golden, 2 to 4 minutes per side. Transfer to a plate and loosely cover with foil. Coat the remaining fish with batter and cook in the remaining 2 teaspoons oil; adjust heat as necessary for even browning. Serve immediately with Mango Salsa.