Preheat grill to medium heat. (If using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for 5 to 6 seconds.)
Toss nectarines and onions with oil in a medium bowl. Season with salt and pepper. Grill nectarines and onions, turning often, until softened, 15 to 20 minutes. Reserve juices in bowl. Transfer nectarines and onions to a cutting board, and let cool slightly.
Combine mustard, vinegar, and chile in the reserved bowl. Cut nectarines and onions into 1/4- to 1/2-inch-thick slices. Add to bowl. Stir in mint, and season with salt and pepper.
Lightly coat both sides of each swordfish steak with oil. Season with salt and pepper. Grill, turning once, until cooked through, 3 to 4 minutes per side. Cut each fish steak in half, and transfer to a serving platter. Top with nectarine-onion salsa.
If the nectarine pits prove difficult to remove, microwave the fruit on high for 20 seconds. This will soften the flesh, making it easy to scoop out the pit.