Ms McNaught said the trees cut most recently had been very large, old macrocarpa trees.
None had protected or heritage status.
She believed the culprits may have been doing it for two reasons.
"I'm pretty sure some of the incidents have been people taking the wood for firewood, whether for themselves or to sell.
"I do wonder whether on a couple of occasions someone has thought they were being helpful by tidying up some straggly-looking trees.
"If people have concerns that a tree or trees might need some work, we'd rather they contact us than take matters into their own hands."
Ms McNaught said there were health and safety considerations.
"There's a danger that anyone illegally cutting our trees could harm themselves or others, both at the time of cutting, and afterwards if the trees are left in an unsafe condition."
SWDC does not grant firewood permits for its parks and reserves.
The only people authorised to trim or remove trees are City Care workers and arborists working under City Care's direction.
Ms McNaught said if people suspected unauthorised cutting of trees on council land, they should call the council immediately on 06 306 9611 or contact police.
She said it wasn't the kind of thing people could do under the cover of night.
"Every time we've had a call about it happening, it's been in broad daylight. If you can provide descriptions and car information, including registration, without putting yourself at risk, that would greatly help us."
