The yaupons are very easy to push out and have shallow roots. I suggest you push them out with the grapple first, then grab them, instead of trying to pull them out.
I'm thinking that if the tractor is big, you will have trouble getting under the live oak trees with it.
I don't think you will damage the oak tree, but just try to be gentle to the surface under the oak tree. Don't try doing this in really wet conditions causing ruts under the tree. Around 90% of live oak roots are in the top 6" of soil, but I would bet that you would disturb only 10% of the surface at most, under the tree by pushing out the yaupon.