Combine first 3 ingredients; set aside.
Heat 1 teaspoon oil in a nonstick skillet over medium-high heat. Add pork; stir-fry 3 minutes. Remove the pork from pan with a slotted spoon. Add 1 teaspoon oil, broccoli, and water to skillet; stir-fry 5 minutes. Add chutney mixture, bean sprouts, garlic, and water chestnuts; stir-fry 2 minutes. Return pork to skillet; stir-fry 30 seconds.