How to remove corroded faucet?
As somebody in your other question noted, you probably have to attack this from the top. A hacksaw will be time (and arm) consuming. An oscillating multitool with a metal-capable blade would be good though slow-ish. An angle grinder would be fast but will also throw sparks and has the non-trivial risk of having the grinder catch and run into stuff you don't want ground, like the backsplash.

Alternately, you might try to drill out a weakness in the nut with either a large drill bit or linked smaller ones. That would allow you to pry it loose.