I guess my first question is what kind of micarta are you turning? Paper, fabric, did you make it yourself or purchase it from an experienced maker?
The paper micarta I've made had a few issues when I hit spots with less resin. They were loose pockets that fuzzed similar to what you are saying. I got around this by adding thin CA to the piece after each pass or two as needed. Even the later blanks that got more resin got CA as needed to keep things more stable.
Also be careful drilling, since heat buildup is a great way to crack the material.
I had better luck with carbide, fresh edge and a downward angle of cut (I didn't have a negative rake insert).