The NSW Game Council has seized on the incident as proof its bid to manage deer culling across the Illawarra should be fast-tracked.

Chief executive Brian Boyle said greater Game Council involvement would "see an end to these undesirable incidents".

"The fact is that this deer that was virtually left on a resident's doorstep was not taken by a hunter - it was taken by a criminal, a trespasser, who deserves to be investigated by police and brought to account," he said.

"A Game Council hunter would have certainly done things differently."

Its hunters were required to seek permission from landowners before hunting and were trained to properly dispose of remains, he said.

Their shooters were also encouraged to use all meat from their quarry, rather than just taking the antlers.

The Game Council has long been lobbying Wollongong City Council for permission to shoot deer - the city's No 1 pest - on council land.

But the group has encountered strong criticism from the Greens and animal welfare groups, who insist professional hunters should be used to carry out the killing.

Greens MP Lee Rhiannon scoffed at suggestions the Game Council should be handed responsibility for deer culling in the Illawarra, describing its programs as "scientifically unsound and environmentally damaging".

"The job of managing the Illawarra's feral deer problem should lie with government experts skilled in evidence-based, safe andeffective invasive species management," Ms Rhiannon said.

A council spokeswoman said it would begin an "expression of interest" process in coming weeks to engage licensed shooters to cull deer on council land.

The process would consider safety, cost, animal welfare and risk management, she said.

The decapitated deer was removed by the landowner yesterday morning.