Yikes!
Steve,
snip now...should the green wire (in the cord going to the new outlet)
also go to the same post as the white / neutral since both are at ground
potential?

No. The green wire (safety ground) is to provide a direct path to 'ground'
in_the_event_of_a_failure. If you don't care if your 110 outlet is
'grounded',
simply leave it unconnected. You will only have an ungrounded outlet.
(Also a GFCI outlet is no good without a ground!)
However, your 220 outlet on the table should have a green or bare ground
wire. If it does not then you don't have a grounded outlet for your saw.
(Don't know why that would be, since it's pretty standard practice
nowadays).

Incidently, your additional outlet idea sounds OK for a lamp or some small
appliance. If you plan on using it for a drill or shop vac with the saw
running, you maybe plagued with CB nuisence trips from too much power drain
on one of the 220 legs.
It might be better all around to just wire the outlet separatly.

Wha'd ya think?
Jon Veeneman