Heat oven to 375 degrees F. Spray large cookie sheet with cooking spray.
If using crescent rolls: Unroll dough; press into 12x8-inch rectangle, firmly pressing perforations to seal. If using dough sheet: Unroll dough; press into 12x8-inch rectangle.
Spread cranberry chutney on top of rectangle, within 1/4 inch of edges. Arrange sliced turkey evenly over cranberry chutney. Sprinkle shredded cheese over sliced turkey.
Starting with longest side, roll up; pinch long side to seal. With serrated knife, cut into 24 slices. Place cut side down on cookie sheet.
Bake 10 to 15 minutes or until golden brown. Remove from cookie sheets. Serve warm.