How long is the piece that broke off?
I had a similar problem once and I ended up getting a bolt that threaded into the clutch, drilled and tapped the bolt for a grease fitting, screwed the bolt in tight, used an industrial grease gun to pop it off. I had to stand on the handle of the gun before it popped off.
Once you get the clutch off you could probably drill a small hole in the broken off end of the puller and then use a slide hammer to get it out.
You really need to take your time on this one to prevent a expensive mess.
Hope this helped!