Preheat oven to 400°
Sprinkle pork with salt and pepper; place on a jelly roll pan coated with cooking spray. Bake at 400° for 15 minutes, turning once. Remove from oven; let stand 5 minutes or until slightly cool. Coat pork with mustard; sprinkle evenly with thyme, pressing thyme into mustard to adhere.
Place 1 phyllo sheet on a large cutting board or work surface (cover the remaining dough to prevent drying); lightly coat with cooking spray. Repeat layers with remaining phyllo and cooking spray, ending with phyllo. Gently press phyllo layers together. Lightly coat top phyllo sheet with cooking spray.
Arrange pork along 1 short edge of phyllo, leaving a 2-inch border. Starting at short edge with 2-inch border, roll up jelly-roll fashion. (Do not roll tightly). Place roll, seam side down, on jelly roll pan coated with cooking spray. Bake at 400° for 20 minutes or until the roll is golden brown and a thermometer registers 155°. Let stand 10 minutes.
Place chutney in a microwave-safe bowl; microwave at HIGH 30 seconds or until warm, stirring once. Cut the pork crosswise into 8 even slices using a serrated knife; serve with chutney.