I have a Grizzle wood lathe and have been trying to use it to turn my cork handles. My problem is the mandrel spins when i put pressure on the cork. If I tork it down, the mandrel bows. What added attachments should i add to the headstock and the tailstock that will allow me to turn the cork

Mudhole ,Mandrel wax works great .

What type of chuck do you have on your lathe? You need some type of scroll chuck on the headstock end. Your mandrel shouldn't spin or slip in such a thing.

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I like a 1/2" Jacobs drill chuck to hold my mandrels. You can crank it down tighter that a regular 3-jaw lathe chuck. Both are however very handy to own. I use my 3-jaw chuck to hold my wood handle blanks to center drill with the jacobs chuck mounted in the tailstock.

I agree with Dick.
The use of the 1/2 inch Jacobs chucks work very well for holding mandrals.

I don't know what type chuck you are using, but perhaps you can use a different set of jaws in your chuck.

Or, you might need to resurface the face of the current jaws in your chuck.

Depending on the chuck, some jaws are pointed, some are flat, and some are curved in the jaw holding area.

Normally, a flat finish on the end of the jaws will hold just fine.

Let us know what sort of chuck you have on the lathe right now. Perhaps we can suggest a fix, or suggest a differfent chuck.

What is the thread size for your particular chuck?

Take care
Roger

p.s.
I just came in from the shop after having turned a bunch of handles on the lathes.
I use a Taig Chuck with soft aluminum jaws with a circular cutout in the face of the jaws and they do an excellent job of holding virtually any size manderal.