Combine the pineapple, onion, cilantro, jalapeño, 2 tablespoons mint, and 1/4 cup lime juice in a medium bowl. Set aside.
Combine the cumin, salt, red pepper, and 1/4 cup lime juice in a small bowl. Pour over steak and let stand for 5-10 minutes.
Grill the steaks, with grill lid closed, over medium-high heat (350-400 degrees F) for 8-10 minutes per side. (If broiling steak, place steak on rack of broiler pan. Broil 6-8 minutes per side, 3-5 inches from heat.)