The wire in the mix is what kind of makes the project nasty for you. Not many machines I know of will not get tangled up in it. I have unfortunately run over old fence wire mostly buried in dirt with an old brush hog, and it made a fantastic knot under the deck. It took a lot of time to get it off, only to find it ruined the bearings so the transfer case leaked oil.
I would nuke the fence line with Glyphosphate, wait until the vegetation dries, and then lay down a line of diesel-soaked burlap bags along the fence line along with other spare brush to burn the whole line off. The hope would be to burn off enough vines to allow tie up of the wire and drag it off into an open area with a truck. Roll the wire up on remaining fence posts and dispose or complete burning and dispose.
And yes, if you are not bleeding (within reason) or don't have a messed up back after working, you are doing it all wrong.
