Witnesses saw a group of four boys, thought to be in their late teens, firing at the duck with a catapult – and immediately reported their concerns to the RSPCA.
The attack happened at around 5.30pm on May 8, at Bumble Hole lake in Netherton.
The duck was later found with her neck bent backwards and unable to stand – and was rushed to a vet who discovered she had been struck several times.
RSPCA Inspector Fiona Howell, who is investigating for the animal welfare charity, said: “This mindless, intentional act of cruelty will have caused this duck significant pain and suffering before her death.
“We share our space with wildlife and need to show respect and kindness. Animals feel pain, just as we do.
"It’s disgusting to think that these young people were taking pleasure from repeatedly firing rocks from a catapult at a living creature.”
Anyone with information about the attack on the duck is encouraged to contact the animal welfare charity’s inspectorate appeal line on 0300 123 8018.