If you are getting an .exe to open on the Android SDK you did not install the correct one. Mine came in a .zip also that extracted the tools nativity for linux. It comes with an eclipse icon you click on for that interface inside of the "eclipse" folder after extraction. Mine was called the "adt-bundle-linux-x86_64.zip" since I got a 64 bit computer. http://developer.android.com/sdk/index.html
The android platform tools themselves do not have any .exe for you to open, either. Lets look over this link above for you to start developing on. It should be called an "ADT bundle for linux" if you are downloading it from your Linux mint build through a browser.
Just extract it in your home folder with your archive extractor that comes with linux mint or change directory into the folder you want it in after downloading. Two folders will extract, one will be labeled "eclipse" and the other will be labeled "sdk", that folder has the platform tools in it for building android modules and such. Just move it into your home directory and double click on it and it will extract into its own self made folder.
Then open up your eclipse folder and click on that icon in there, after it is extracted, eclipse is piggybacked on the other android sdk tools and will set it up for you with its own onboard repository for its own tools.
Hope that helps you.