We had the mirror image situation here in the ACT. The committee wanted to keep a large tree that a unit owner was lobbying hard to remove.
First, find out if the tree is a ‘regulated’ tree (or similar term). In the ACT any tree over 12m or more than some particular girth is automatically a ‘regulated’ tree and permission to remove it is required from the local government. You might have something similar.
Any owner can put a motion on the agenda with enough notice. Put a motion that the tree not be removed unless local council permit it and two arborists say that it is unsafe in a way that cannot be remedied.
Alternatively, if removing the tree is only put as one item of the budget motion, round up people who will only pass the budget after an amendment to remove that line of the budget.
You could apply to your equivalent of the Civil and Administrative Tribunals of other states for an urgent stop order until the matter has been put to a general meeting with sufficient time for parties to gather the requisite information. My experience of the Tribunal in the ACT is that it is keen to seen matters such as this fully aired at a general meeting and opportunity given for the democratic process to decide the matter before it imposes a decision.