You cut the cast iron with a reciprocal saw like a Milwaukee Sawzall all. Use heavy metal blades like Lenox 614R type. I start with the six inchers. It will take several to get through the side of the pipe . Once you have made a cut into the pipe - it will go faster. You'll need the long metal blades to finish the job. At first-it will seem like it will never cut it-but it will. Use Mission or Fernco No Flex couplings- one on each side-to connect the plastic and cast iron. Do not forget the vents!

In most situations I use a Ridgid rachet cast iron cutter on iron waste pipes, but sometimes conditions are too confined to use that tool. Then I use a mini-grinder with a diamond wheel (they're $100 each but one lasts a lifetime) to cut as much as I can reach with that tool and finish the cut with the sawzall and a grit-edge blade. BTW the grinder with the diamond wheel is terrific for cutting tile, concrete and brick. A little dusty though.