That may not be the best way to do it and I may not have described it well but that is what has worked for me.
If the soil in your pot isn't real loose, probably the best way to separate the sucker from the mother plant would be to cut a circle straight down into the soil with a knife all the way around the new plant (about a couple inches away) cutting through whatever roots are there. Then lift out the plug of soil and roots along with the new plant. Be sure to fill the void with new soil.
Good luck if you try this! I would feel terrible if you damaged your precious plant!
You could also go to a local nursery and get more professional advice to make sure.