To prepare sauce, combine first 7 ingredients, stirring with a whisk until sugar dissolves; set aside.
To prepare spring rolls, add hot water to a large, shallow dish to a depth of 1 inch. Place 1 rice paper sheet in dish; let stand 30 seconds or just until soft. Place rice paper sheet on a flat surface. Arrange 1 lettuce piece in center of sheet. Top with 1/4 cup sprouts, 3 carrot strips, 3 cucumber strips, 3 bell pepper strips, 4 shrimp halves, and 3 mint leaves. Fold sides of sheet over filling; roll up jelly-roll fashion. Gently press seam to seal. Place spring roll, seam side down, on a serving platter (cover to prevent drying).
Repeat procedure with remaining rice paper, lettuce, sprouts, carrot, cucumber, bell pepper, shrimp, and mint. Serve with dipping sauce.