That is a 3" stack, which under most codes will be capable of handling another bathroom. Not knowing the venting scheme for the existing bathroom that is already draining into this stack, you will want to tie in beneath the existing bathroom. The pipe can be cut with a snap cutter, or if you can access all sides of it, with an angle grinder. I would be wary of the angle grinder option, because it creates a lot of sparks, an definite fire hazard in any home, even more so in an older home with really dry wood. You might be able to rent a snap cutter somewhere. Whatever method you use to cut it, you must make certain to support the piping above the cut really well. The piping is very heavy, and WILL come crashing down.
This is not a simple project, so if you are thinking about DIY, make sure that your skill level is up to it. You will also definitely want to pull a permit and get it inspected, just so that a trained pair of eyes will make sure that you have everything installed correctly.