Easiest way to do it is disavow all the crappy links and do a resubmission.
It's not an overnight process, you'll be looking at a good few weeks, maybe even a month or two before you get back in the index. The important thing to know is it can be done - I've gotten a few sites back ranking after being pinged for crap links.
My advice would be to spend that few months of downtime building a new website. Go easier on the spam and hopefully, you'll end up with a cleaned up site back in the index plus a whole new site ranking too.
If this is your only website, treat the v&nning as a wake up call. You need to diversify your sites, offers and networks you sell for.
My 2 cents anyway.