What I've done before is to set the cutter so that it doesn't protrude all the way through and so it won't fall on to the cutter and ruin the job. I then carefully finish the rest of the cut on the bandsaw, leaving enough on to tidy it up with a hand plane.
Dude - I'd go down this route too, get your depth cut just right so you don't go right through then use a sharp blade (stanley knife) or as OPJ says-a bandsaw to finish off the cut. If you haven't got a plane, I've found a good flat sheet of sandpaper will suffice.
Good luck
Mark