Do I need to dig out ground Palmeto Palm to eliminate it..

from my yard?
Or is a chemical called for. How do I get rid of ground Palmeto Palm. I live on a hill and I need to remove it to put in a new bed. The Palmeto are very few, maybe 6.
Need to know how to tackle their removal.

probably need to use all the methods you have listed as well as burning, they are tuff to get rid of, deep roots, or just keep taking the leaves off for the nex 10 yrs til it might give up.