This is not possible automatically. You will always have to take some "step" to hide the tags or data in the tags you don't want to see before printing.
This is one reason we see a lot of users create "Printing" and "Working" views in their models. Printing views are "locked down" to show exactly what needs to be printed, but working views are there for reference and getting work done.
I have seen some folks make a tag or part of a tag in yellow... but this is really only effective when you are actually printing. PDFs show it pretty clearly.
