...I'm with Doug...outsiders call this "frame damage," but its all about shaping the monocoque, and this means a really big pull on a frame machine. The good news, that part of the job is only labor intensive--a world of chains/clamps, torches and sledgehammers, with a goal of stretching the hulk back to where the rear of the doors finally fit, ending when the windshield sits flat. And only then comes the bodywork. The bad news are the wrinkles over the driver's side and the extra wide gap at the front of the passenger side.
No, I don't think that the car would be doomed to driving a little sidewise or leaking in the rain...and the alternative (parting the car out) will not recover a third of what the car was worth before...But history won't curse the owner for scrapping it out--even a Mangusta is not truly a rare car. Its really a matter of what you want next.
So if you have parts lined up (and I would include a straight roof, structurally the car will need to have some members that are not wrinkled to death) the next path would be to strip out the seats and maybe even the engine so the sado-machinist work with the torches and chains could be tried...its been 35 years since I've been around this stuff, but I'd think after a couple thousand dollars on a frame machine, whatever decision you'd make then to go forward would be more clear...