Cypress Knees

Yes, you can remove them without harming the tree. But realize that you are setting yourself up for future problems: the tree will continue to throw up knees wherever it likes. Be sure you are pouring a thick enough patio extension with remesh/reinforcement so that you're not dealing with cracks a couple years down the road.

I looked at a property in Old Mandeville and there are cypress knees in the middle of the backyard where I would want to put a pool.

The realtor told me I could "sneak out there at night and chop them out of the ground." I asked her what she meant and she said that the Old Mandeville P&Z Committee would never allow me to remove them but I could probably get away with doing it under the cover of darkness.

So I guess the "can you" question is relative.