I use a set of Fiskers scissors. Normally used for sewing, they are sharp as h3ll, make a very clean cut, and don't dull.
I have however sliced a finger so deep that it has no feeling in the end (which comes in handy when moving hot things around on the BBQ)...so due caution noted.
Once you have your rough disk cut out, use testors model glue to glue the plasticard to your base. Let dry/cure fore a few hours.
Then use an exacto blade to trim the excess right up to the edge of the base.
Then attach model, prime, paint, etc in whaterver order you do your bases.
This is the HO scale diamond plate with some plastic strips and 1/8" rod for details.