Heat 1 tablespoon oil in large skillet over medium heat. Add shallots; sauté until softened, about 5 minutes. Add garlic, 1/4 teaspoon coarse salt, 1/4 teaspoon thyme, and 1/8 teaspoon allspice. Stir until fragrant, about 30 seconds. Add blueberries, 1/4 cup water, and vinegar. Stir to blend. Mash berries with potato masher or back of fork and cook until sauce thickens, stirring often, 3 to 4 minutes. Season with freshly ground black pepper. Remove from heat. DO AHEAD Can be made 2 hours ahead. Let stand at room temperature. Rewarm before using.
Brush grill rack with oil. Prepare barbecue (medium-high heat). Brush salmon on both sides with oil; sprinkle with coarse salt, thyme, allspice, and black pepper.
Grill salmon until just opaque in center, 4 to 5 minutes per side. Transfer to plates. Stir 2 tablespoons sliced mint into warm blueberry sauce. Spoon sauce over salmon and sprinkle with remaining 1 tablespoon mint. Serve immediately.