Are you talking about a laminate, fabric or prepreg? If it's a laminate, do you know what the resin is?
Hate to answer your question with questions, but....
After re-reading your post, it appears that this is already laminated. Standard carbide end mills will work most of the time. I have encountered only a few composites that were extremely difficult to cut and for those, diamond tooling was used to basically sand the part to shape. I have turned end mills into semi-molten blobs trying to cut composite armor plating so I can attest that it can be a challenge. Most of the cutting I did was with either dry fabrics or pre-preg materials but had to rout laminated panels from time to time and I would typically use Micro grain, high helix end mills and adjust as necessary to keep the tool from overheating. Watch the dust.