Rinse salmon fillet, pat dry, and lay skin down in a rimmed pan.
Mix sugar with salt, curry powder, and dry mustard. Pat mixture evenly over top of salmon. Cover and chill 1 to 3 hours. (Coating dissolves.)
Peel and thinly slice onions. Chop enough mint to make 2 tablespoons.
In a bowl, combine onions, chopped mint, and vinegar. To serve within an hour, add ice. If making ahead, cover and chill relish up to 3 hours; stir occasionally.
Rinse salmon under cool running water, rubbing gently to release salt. Set fish, skin down, on a sheet of heavy foil and trim foil to fit outline of fish.
Prepare grill for indirect heat.
To use charcoal briquets, ignite 60 briquets on fire grate. When dotted with gray ash, in 20 to 25 minutes, push half the coals to each side of grate. Position grill about 6 inches above grate.
To use a gas grill, turn heat to high, close lid, and heat for at least 10 minutes. Adjust heat for indirect grilling (no flame beneath food).
Set salmon in center of grill, not over hot coals or flame. Cover; open vents on charcoal grill. Cook until fish is opaque but still moist-looking in thickest part, 12 to 15 minutes.
Slide a large, rimless baking sheet under fish, then slide fish onto a platter.
Sprinkle with remaining mint leaves. Lift portions of fish off skin.
