Hard to say what's going wrong here. Most likely, you don't have permission to save to the volume/the folder you wanted to save to. (Perhaps, because it is a network share where you need to log on first, for example...)
However, from the information at hand, this is just a guess.
If the problem persists, you can send the error report that you are getting to us. It contains the complete stack trace and information about your environment (yEd version, Java version, Mac OS X version); this will help us.
I'm not sure, but I think it doesn't include where you are attempting to save to, but this is an important piece of information, of course.
(Don't forget to include your email when sending the error report, so we can reply.)