2" vent pipe rusted out?

Hi,
I was replacing a pedestal sink that was installed incorrectly and made a hole in the wall to add a backer board. I've attached a picture showing the hole, and then another showing the bottom of the pipe where the rust occured. This is a second floor bathroom and the pipe is just above the hole in the wall below the mirror. It seems to run horizontally from the stack in the corner which is to the right past the toilet to the end of the wall ,and then goes to the basement. It seems in the basement it is just capped. So I was told I can just cap it. Is that correct? Should I be worried about damaging the stack if I cut the pipe with a sawsall? The pipe is mounted in the wall going through round holes in a 2x6. I was worried that it might be used for a vent for the downstairs bathroom as well. Could that be the case? These are the options I can think of. Are they correct or what would people recommend.

1. Cut the pipe out and cap it like suggested.
2. Cut out the bad section of pipe and replace it was a section of PVC and use the Fernco to join the galvanized pipe with the pvc.
3. Use epoxy to fill the rusted out section of the pipe
4. Cut a fernco so I can put it over the rusted out section and clamp it down.

Any suggestions would be helpful.

From your description, we do not know if the pipe is serving any purpose.

Looking at the picture leaves me wondering where the vent is for the pedestal sink?

NOthing you have written helps us to decide what you should do, or if you even have a problem. Where is the "rust" and is it just on the surface of the pipe?