That's what I'd envisioned and the reason I'd suggested a b-i-g boltcutter - the bigger the better - so as to cut multiple sections at the same time.
Fasten a fence-stretcher to the bumper hitch and to the section going into the water, cut the wire above the stretcher, then drive as far forward as possible. Cut and coil.
"Carve" through the tangles and collect the pieces.