Well first off your CMS is usually NOT accurate enough for this. A CMS is designed to cut molding for trim, not picture frames. When you cut moldings you only need two pieces to mate and the miter is on the narrow portion of the wood. An error of ½° in the saw is invisible. But when you cut a frame the errors are cumulative so with eight miters that same ½° is multiplied into 4°. Additionally the miter on the frame is on the wide part of the board so the angular error has a longer baseline to work on and you get a significant gap.
Professional frame shops use a "Lion Miter Trimmer" which is a precision knife that you use to 'clean up' the cut from your CMS into a "perfect" miter. Rockler has it in their catalog:
#22460 - Lion Miter Trimmer - $270
This is a *very* expensive tool for just occassional use.
For beveling edges on small boxes you can get a router bit with a precision angle on it. You should precut the bevel on the TS to get it close and then use the router bit as a "clean up" to give you a precise angle. They are available in other angles as well so you can cut hexes, octagons, etc.
A company near us produces molding of all shapes and sizes. They have perhaps four people looking over plans and doing takeoffs, then bidding the molding for the jobs. Given that, it may be useful to...