You can probably find some footage of the Jigsaw puppet on YouTube. Download the footage, record your haunt rules, and use a video editor (Windows Movie Maker works just fine) to sync the puppet with the audio. Don't worry if it looks jerky. Jigsaw's videos are generally jumpy and plagued by static. An amateurish look will actually add to the authenticity.
Either that, or build a jigsaw puppet head yourself and record the video that way. If you do it this way, run some kind of static or old TV video filter over the footage to give it that iconic Jigsaw look.