Ms Penman said the remote-controlled jet boat, which was about a metre long, broke the swan's wing, ribs and leg.
"Its wing was bleeding. I came home and rang the police."
Meanwhile, the jet boat owners had refuelled the boat and steered it after a flock of ducks, fatally maiming one, Ms Penman said.
The next day Ms Penman said she tried several times to capture the injured swan with friends and SPCA staff.
They eventually succeeded by throwing a towel on the swan's head. A veterinarian later euthanised the bird.
The jet boat owners were described as aged 45-60 and wearing shorts, dark T-shirts and black jandals. One had brown hair and a full short grey beard.
Any information should be passed to the Napier SPCA.