How can I disconnect rusted tail piece mount from popup flange?
You need a spud wrench to hold the upper drain flange (which is threaded to the lower drain assembly) so you can unscrew the drain from the flange.
Cheap ones (which are hard to hold) look like this:

Good ones (which are easy to hold with a large wrench) look like this:

And like it or not, you need a helper to either hold from above or turn from below whilst you are doing either.
NOTE- there are many tools colloquially called &quot;spud wrench&quot;, these are plumbers' spud wrenches.
NOTE- I have substituted for a spud wrench in a pinch by sliding my ChannelLock plier handles down into the strainer from above, as a holding tool.
NOTE- sometimes none of this works, that's when I use a mini-hacksaw to cut relief slots around that upper drain flange and break it off.