I have clipped my data frame based on city limits. One ortho has a tranparency and is excluded from the clip, I added a different ortho without trasparency and did not include itin the clip, so the ortho appears more vivid inside city limits. Everything in my layout looks exactly the way I want, but if I export the map or print the map there are additional areas in the vivid ortho that show up outside or the clipped area.
I ran into the same thing. The clip won't work when printing. Its a known problem that I think they are trying to solve. There are other forum posts on this, but I couldn't find them in a quick search. My advice is to find another way to highlight the boundary. I've created a "mask" of everything outside the boundary and then made that transparent to make everything else fade.