Prepare outdoor grill for cooking by the direct heat method.
Whisk together honey, mustard and mint in small bowl and season with salt and pepper to taste.
Place ground turkey in a medium bowl and season with salt and pepper. Divide ground turkey into fourths and shape into patties about 4-1/2 inches in diameter. Brush both sides of the patties with honey-mustard glaze and place on the grill. Cook until golden brown on one side, about 5 to 8 minutes. Turn over and continue grilling. Glaze each side one additional time while grilling. Grill burgers about 15 to 20 minutes or until meat thermometer inserted into center reaches at least 160 degrees F.
Meanwhile, brush the slices of pineapple with oil and grill for 1 to 2 minutes per side or until golden brown.
Place the buns on the grill and heat for 20 to 30 seconds. Remove from the grill and place a burger on the bottom half of each bun. Top each burger with a slice of pineapple and arugula leaves.