Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the jalapeños over direct medium heat, with the lid closed, until blackened, about 10 minutes, turning occasionally. Place the jalapeños in a bowl and cover with plastic wrap to trap the steam. Let stand for about 10 minutes. Peel away and discard the charred skin, stems, and seeds, and then finely dice.
In a small saucepan over medium heat, cook the butter until melted and frothy. Mix in the jalapeños, mint, lemon juice, scallions, and ½ teaspoon of the salt. Keep warm over very low heat.
Brush the swordfish steaks on both sides with oil and season evenly with the remaining ½ teaspoon salt and the pepper. Grill over direct medium heat, with the lid closed, until just opaque in the center but still juicy, 8 to 10 minutes, turning once.
Top the swordfish steaks with jalapeno-mint butter sauce and serve warm with lemon wedges.