Heat grill or grill pan to medium-high. In a bowl, combine plums, sugar, lemon juice and 1/8 tsp of the salt.
Rub mahi mahi with olive oil and season with remaining 1/2 tsp salt and the black pepper. Grill on medium-high for 5 minutes. Flip and grill another 3 to 4 minutes, until fish is cooked through.
Stir basil into salsa; spoon salsa over fish before serving.