you can, however, cut all the branches off. Looks awful, but no more leaves, acorns and assorted crap. It will eventually grow back all it's branches over time. I had 2 in my neighborhood do this exact thing. No idea of the price. It's a temporary solution that doesn't need ARC approval

Small trees, usually for purposes of sizing for sale, are measured just above the bulge above the soil, so at about 4". That's called caliper measure. Larger trees are measured at Diameter at Breast Height (DBH). That measure is used for things like ascertaining value for an insurance claim, and dosing for pesticide application. Yes, I am an ISA Certified Arborist, but I am from Colorado. Not many Live Oaks around here. I have one Live Oak in my yard in The Villages that has an obvious lightening strike. I understand that I can take that one down, but never a healthy one.

Oak Tree
 

Doubt you'll get permission unless it is diseased.

Most people who can't get permission have it "trimmed" excessively so all that is left is the trunk and a few branches. New branches will come back, but it will solve your problem for a while.

Oak tree removal
 

Tree Frog : whatever they do GET IT IN WRITING FIRST

Oak tree
 

This will be me in a year. I had the tree cut back this year but it grew very fast. Tree is healthy but the lawn around is is having trouble growing. I had a neighbor complain last year when during a windy day some stuff blew on to their driveway

Depends on location
 

Our tree guy told us it was okay to remove all the branches. In Lady Lake it was not. We got a letter from the town, had to go in to discuss. Then we had to go to ARC and get permission to remove it. Our new tree guy, an arborist, was able to help us through the process. He was able to prove that the tree roots were causing damage to our property and potentially the water lines at the street, so both the town and the ARC approved removal. We had to prove also that the tree was not healthy enough to come back from the extreme “dead- heading “ that the first guy did. We were not fined, but we spent several months in limbo, not knowing which way it would go. My advice- make sure your “expert” has experience dealing with the proper authorities for your location. You are not only dealing with The Villages.

When we first moved here sixteen years ago it was against the law to remove a Live Oak Tree that was more than eight inches in diameter.

State law has changed, but you need to fill out forms and get permission.

FAQ: Why Do You Need A Permit To Cut Down An Oak Tree In Florida? - Oaks in Sacred Rocks

Florida law now supersedes ARC approval. If you can get permission from a certified arborist for removing your oak, the ARC has nothing to say about it.

I been told I have a "water" oak tree in my back yard, is there a difference between oak and water oak?

Oak Tree Identification
 

This will help you in identifying various oak trees:

:1rotfl:

And you are wrong about that. Florida law supersedes local governmental regulations but it does not supersede private contractual obligations. You as a homeowner here have agreed to abide by rules that are more stringent than Florida law. You are legally bound by the contract you signed which includes rules about removal of trees.