I will assume the BB in knackered which is why you are trying to remove it.
This is what I would try.
Get some WD40 or plusgas on the thread from the inside of the BB shell. Let it soak overnight. It may not be overtightened but corroded threads binding it up. The damage to the cup may be the previous owner trying to get it out before hand. Who knows?
Pop the other cup back in and nip it up, not tight.
Slide the crank back in with the chain rings on the other side. This, and the other cup will serve as a guide to ensure that the tight cup will stay square when you are flogging it.
Use a pipe wrench on the damaged cup. A pair of stilsons will grip the cup more as you apply force.
Start gently and then gradually build up to ‘get the **** out you b******’ type tapping with hammer.
Do make sure you are undoing it the right way! Right hand cup, left hand thread. Left hand cup, right hand thread.
P.S. I have not actually had to try this method and don’t want any blame if it goes wrong. If in doubt, LBS.
Best of luck. :wink: