How can I express my dismissal from public service in my academic resume?
I think that under the circumstances you can just tell it truthfully and completely. The recent political turmoil in Turkey was widely reported here, and I think most people would both understand and sympathize with it. 

You might also point to the fact that you weren't alone and that the dismissals had nothing to do with the competence of those dismissed. There are plenty of news stories that could be noted. 

We aren't perfect here, but so far, our political institutions are holding up.