A concerned member of the public, who wished to remain anonymous, sent a copy of the video to the Herald. The person said it occurred in Christchurch on Saturday, July 28.
The Herald understands the video was shot by a pupil at a Christchurch high school.
The video has been shared widely on social media application Snapchat.
SPCA CEO Andrea Midgen said they had been sent the footage several times and had referred the incident to their inspectorate for investigation.
"These recent videos only highlight to us just how critical it is to educate our future generation of New Zealanders, and break the cycle of cruelty in our country," Midgen said.
Research showed a link between human and animal abuse, she said.
"The SPCA believes there is a real need to create behavioural change in New Zealanders' treatment of animals."
The SPCA had launched a free education programme for New Zealand schools, which aimed to encourage empathy towards all animals and to people.
