"These are not isolated cases," the woman says.
"He is deranged, dangerous and he will do it again," she added. "It could be cats, it could be dogs ... it could be kids."
On both occasions, the man, who the witness believes to be a local from Mt Albert, rode off on his bike with the dead bird.
The SPCA says it has assigned an officer to investigate the incident.
This is now an active investigation and an Inspector has been assigned to follow it up," a spokesperson told the Herald.
"Without an address of the person who allegedly killed the pukeko, it will be difficult to find the person – especially because he was riding his bike around the neighbourhood.
"We would encourage anyone with information about the person responsible to call us and make a welfare complaint."