How can I remove the part of a old shut off valve from the pipe under bathroom sink, including the ring on the pipe?

Hi Nick...

Are you asking how to remove a nut and ferrule (see images)?

If so, you can purchase a handle puller with a ferrule/nut removal attachment (see other image).. only thing is the handle puller must have the ferrule/nut attachment end as shown in my picture. Check it out @ Superior Tool PLUMBERS PULLER KIT - Product Reviews and Prices - Shopping.com They are available at home depot and Lowe's, too.

If you have a mini hacksaw and the ferrule isn't too compressed you may also be able to cut across the ferrule and remove it that way... the nut would just slip off after that.

Finally, if you are just installing a new compression shutoff then you may simply be able to reuse the old ferrule and nut.. try it out and see what happens, right?

Back to you...

Mark