You can certainly use a reciprocating saw or grinder with carborundum blades to cut CI drainpipe, but it is far better and easier to use a "snap cutter." You need to make sure the drain pipe is adequately supported before you cut into it. You can make the connection to plastic pipe using special compression fittings. Fernco makes the widest and most useful selection of these.
You can DIY but I'd suggest you bring in someone more knowledgeable to give you advice. The snap-cutter may be rented if you don't want to shell out the $300 or so that these cost to buy.