What is the best way to remove concrete flooring section in a bathroom? We found a broken rotten rod iron drain pipe when tearing out walls for remodeling and unfortunately (blessing) found out the pipe was rotted. Plumber says to replace with PVC but we have to dig up/cut up the floor ourselves. What can we use to cut the floor safely and easily?; any suggestions would be helpful.

Yes, depends on access to area to remove. Using a concrete saw works great but be able to contain the dust by venting out the window, putting up a plastic visqueen curtain for confinement and possibly using water. The powder will fill your house if you don't. Take care on cutting deep. Slab depth is usually 4" thick. Plumbing may be below in the fill. If that pipe was so badly eroded, then there may be more and consider replacing all of it.
Next, if you are into exercise and sledge hammers great, if not rent a jack hammer. You will be happy you did if this turns out to be a big job. Nm