The CODC believes the robinia tree was attacked on Friday night, with the tree then consequently removed due to a safety risk.
It was reported to council by a contractor the following day and has since been reported to police.
In a statement, the CODC said it was "really disappointed to discover that someone has taken it upon themselves to attack this tree in Alexandra Cemetery recently".
"For public safety, we’ve now had to fell it."
The council also confirmed damage to speed signs on either side of the road into the cemetery. It is unclear if these are related.
A council spokesperson said to the CODC’s knowledge, there had been no prior complaints or issues with the tree.
Council parks and recreation manager Gordon Bailey said there would be a replanting, with the timber to be given to the Salvation Army for firewood.
The cost to ratepayers for removal, cleanup and replanting was estimated at about $1000 to $2000, Mr Bailey said.
Community members have taken to social media to express their sadness at the loss of the tree.
In a Facebook post, the CODC notified the public of the incident, with many expressing their frustrations.
CODC is reminding residents that cemeteries are places that should be treated with respect.
"A cemetery should be respected as a sacred resting place for those who are no longer with us," the statement said.
"If you have concerns about any trees on council-maintained land, let us know. Please don’t try to cut them down or trim them yourself."
Anyone with information is urged to contact council or police.
