With the thread stripped there should not be much holding the nut in place so I would try drifting it out. That is, find Drift Punch (or similar object) with a diameter small enough to pass through the nut. Apply Drift to middle of bolt and tap it with a hammer. Start tapping gently and stop well before there is any danger of damaging bridge/frame if it doesn't move.
Otherwise splitting the nut is best option. There are specialised nut splitting tools for that that might be easier to use. But with a bit of care, it is also possibly to use a hacksaw or Dremel tool for the job as suggested in other answer.
Addendum - another possibility - maybe ...
One other possibility occurred after Criggie's comment ...
If there is enough play behind the nut to insert a thin prying object e.g. old flat bladed screwdriver, then sometimes it's possible to persuade what remains of a thread to work well enough to undo the nut one final time.
To do this, insert and use the pry to exert a gentle removing force on nut. Again be careful not to damage frame. Based on pictures best location for this would be the stack of washers on the opposite side of the bridge to the nut. Then while exerting the pressure with the pry try undoing the nut 
 Using a socket set will makes this two handed operation a bit easier. As will persuading a friend to join in with the fun.