My wife and I noticed that the lineoleum floor around the toilet in our 1/2 bath was bulging and splitting, which indicated that there was water damage to the subfloor. When we removed the linoleum we found that the plywood subfloor was completely rotted and wet. We removed the subfloor down to the floor boards. The drain pipe which extends up from a cast-iron bell connection was corroded and soft. I'm in the process of trying to remove this pipe and am finding it to be very difficult. I've damaged the pipe beyond repair, so I've passed the point of no return. I need to get (or cut down, if possible) this 4-inch pipe (which I believe is lead) out of the cast iron. I've created a vertical cut into the pipe down to the cast iron, but am having trouble trying to separate the lead pipe out of the cast iron. Is there any easy way to do this, or is there any tools that will help with this?

You have a lead raised coming out of a cast iron bell. Correct? The lead raiser is secured to mthe cast iron by a lead and oakum poured joint.
To remove a poured lead and oakum joint take a 3/8" drill bit and drill a few holes down past the lead and into the oakum.. Push a screwdriver under the lead ring and lever it up. Once it's free you can began to peel the lead ring out. Now pick out the oakum and you can pull the joint apart.
You will have to get a piece of cast iron for your new raiser and a new closet flange. The cast iron piece can then be Poured and caulked and a closet flange installed. Good luck, Tom