You sure you have to take down the entire tree - can't prune out the disease? For an extreme infestation I can see your point.
Perhaps wait a season and see what the tree produces, you might be surprised. No tree is perfect.
Sounds like Black Know Disease?
You can bury the limbs without spreading the disease.
You can burn green wood as well, it doesnt take too much dry wood once its going. Use a propane weed burner followed by a leaf blower.