Going back to basic chemistry: Presuming it's good quality natural rubber, basically nothing is going to dissolve it (or rather nothing safe, e.g., with suggested methylene chloride being carcinogenic).
But presuming it is good quality natural rubber, likely for a chemistry stopper, you should be able to relatively easily cut it up by melting it. For example, heat a knife blade in a flame and keep pressing it into the stopper until it's sliced in half, or cut pieces off. This should be done with good ventilation, since besides melting, you'll likely also be vaporizing and combusting some rubber.
Or maybe put the whole assembly in your oven at as high a temperature that's needed, with the piece upside down so the rubber/plastic melts and flows out, or surely will soften enough to be easily attacked.
But presuming it is good quality natural rubber, likely for a chemistry stopper, you should be able to relatively easily cut it up by melting it. For example, heat a knife blade in a flame and keep pressing it into the stopper until it's sliced in half, or cut pieces off. This should be done with good ventilation, since besides melting, you'll likely also be vaporizing and combusting some rubber.
Or maybe put the whole assembly in your oven at as high a temperature that's needed, with the piece upside down so the rubber/plastic melts and flows out, or surely will soften enough to be easily attacked.
. I like the previous poster's idea about the long drywall screw. If the screw is long enough you should be able to grab it with some pliers and pull it out of the end if well lubed. Maybe something to stab into it to keep it from spinning when trying to screw in.
. Safety glasses are a must, maybe even leather gloves. I'm sure there is some chemical that will work but is that what you really want to vape after? 
