Closet flange removal

I need to remove the current closet flange in order to tile the floor and install a new closet flange on top of the flooring. I'm assuming I need to cut the pipe? I was able to unscrew the flange from the floor, but I can't unscrew it from the plastic pipe. I guess it's glued and the only way to remove it is to cut it.

I have two questions. First, where should I cut the pipe? just under the flange?

Second, if I cut the pipe, will I need to get a drain pipe extension and coupler for the new flange (which will be higher due to the backer board and the tile)?

Thanks for any advice or redirection.

Plastic pipe is solvent welded (think the glue you may have used to assemble models when younger)...it melts the plastic to weld it together. So, yes, you need to (generally) cut it off. If you have access from below, you'd want to cut it off a ways down so that you could install a coupler and a new riser pipe. An alternate would be to cut it off then use a Rambit, or similar tool which is designed to ream out the socket the pipe fits into, so you can reuse the elbow or other coupler then just install a new riser. You can get an inexpensive inside pipe cutter to cut the pipe. It's essentially a small saw on a shaft that you use to cut the pipe from the inside.

If you cut the pipe just under the flange, you won't have enough room to install the coupler required to put in a new piece of pipe without the new flange being way too high.

A picture from below would be nice here.
You may not be able to extend to the proper height, depending on the the fittings below.