Heat grill to high. Place the squid in a bowl, drizzle with a few tablespoons of oil, and season with salt and pepper. Grill the squid bodies and tentacles for about 2 minutes per side. Remove from the grill, let rest 5 minutes, then cut the bodies crosswise into 1/2-inch thick rings. Keep the tentacles whole.
Brush the bread lightly with oil on both sides and season with salt and pepper. Grill for approximately 1 minute per side or until lightly charred. Remove and cut each slice into 1/2-inch dice. Brush the tomatoes with oil, season with salt and pepper, and grill until slightly charred, about 1 minute; remove and coarsely chop.
Toss the squid, bread cubes, and parsley with some of the vinaigrette in a large bowl. Let stand for 10 minutes. Arrange the tomato slices along the bottom of a serving platter. Top with the squid-bread mixture. Garnish with torn mint and drizzle with additional olive oil and red wine vinegar, if desired.
Whisk together vinegar, mustard, chipotle puree, honey, and garlic in a medium bowl. Season, to taste, with salt and pepper. Slowly whisk in the oil until emulsified. Stir in the mint. Let sit at room temperature for 15 minutes before using.