With crown molding where the top of the wall meets the cieling, you have to pull it down.
I don't think anything other than a Dremel or roto-zip spiral saw maybe could cut it in place without buggering up the wall more than taking it down would. Unless it's high quality HUGE multi-piece old crown moldings, you won't have room or the depth at the inside of a right angle where the ceiling meets the wall to use a jigsaw or sabersaw either. And even with a Dremel or spiral saw you'll have to do it freehand, standing on a ladder working over your head. You won't get a straight line, and worse, you'll never know exactly where to cut before the cabinets are up, but do it that way, you have to cut first. It's just bass-ackwards to try it that way, and the odds of disappointment are quite high.
So it's indeed AW is right, it's actually much easier to gently pry it down and cut it after the cabinets are installed. Even if the nails rip the wall up badly, it's still easier to patch and repaint the walls than it is to fix buggered up wood.
If the trim has been painted over several times, first score the edges between the trim and the wall and cieling with a razor knife to break the paint bead.
Then use a thin sharp trim work flatbar prybar and carefully get it underneath one edge. Use a block of scrap wood underneath the fulcrum of the prybar to spread the load out so you don't dent the wall and cieling. Take your time, move around to different places on the crown molding so it comes off evenly and doesn't bend too far in any one place. Once it's down, gently pull the nails out, it may be easier to pull the tiny-headed finish nails through than back them out, and you can always putty the holes and/or repaint.
