As small a difference as 1/16" between the mount board and the window mat shouldn't be a problem, particularly, if the intention is to frame the work. It might be a problem if you want to hinge the two together for unframed or portfolio purposes. Cutting as little as you suggest cleanly can be next to impossible with rag board. Unless it bothers you, it's probably best to leave well enough alone.
FYI: "backing board" is the term for the scratch board one puts under the board to be cut so that the cut will not become ragged.
BTW, when I called Logan's customer service, some years ago to inquire how to predictably bevel cut corners with their machines, the fellow on the other end admitted that all the bevel cut measured markings on their framers were not to be considered accurate. He further began a rant about how it takes years to properly cut mats and frame, this from a representative of a company which sells mat cutting equipment for non–professional and home use. It was in large part from my memory of this unwarranted interaction that I wrote Print Presentation. With proper "amateur" equipment, sharp blades, planning, and a little bit of care, anyone should be able to cut professional looking mats with a bit of practice.