Wrong answer. That does not keep a fault between the neutral and ground
from lighting up the frame of the saw with 110v.

not pleasant...what might cause such a condition?

You need to have a four
conductor plug and wire, and the white wire on the 110 plug should be
completely separate and isolated from the ground connections of the saw
frame.

So if I connect the white wire from the new outlet to the 220V outlet's
centre pin (neutral), this will essentially put the white wire on the saw's
frame?

The ground of the 110 should still be connected to the ground of the
saw.

If I connect the green wire from the new outlet to the metal box of the 220V
outlet will this still cause a problem?

To be completely right, the receptacle should be wired with 4 wires, all
the
way to the box, with separate ground, neutral, and two hot feeds.