I’d do it outside just because the black dust gets everwhere.
I cut lots and lots of carbon fibre (talking 1-2″ thick sections) routinely for testing. The main reason for this is to prevent mess and stop you getting in trouble with the OH for walking in carbon dust.
Mark a ring all the way round.
Clamp it carefully (i’d go for the wooden jaws on a workmate or something similarly gentle).
Put some newspaper down to stop you getting black marks on the patio that your cat will walk in (if you have one)
Use a sprinking/spray of water where you are cutting to capture the dust.
Use a fine saw with light pressure to prevent splitting (or if you have a diamond wheel tile cutter they are ideal)
Clean up with damp and soapy kitchen roll and dispose of in the newspaper. If you want to get the dust out of the middle give them a blast through with the hosepipe over the grass.
Now if you are attacking a big chunk of wing/wind turbine with an angle grinder then disposable suit, mask and goggles are a good idea!