all wine corks are not made from cork
I'm not a big drinker here. I only drink when I'm alone or with someone.
I used to collect "corks" from wine bottles and at some point they switched to a composite, plastic sorta stuff rather than cork.
I don't know how this stiff cuts or if it is desirable, so that's another factor. I you are using real cork it will cut differently than the synthectic cork.
Your material may work better sliced than sawn, .... I donno? Check into it and let us know.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)