Click Go > Go to Folder and Open ~/Library/Application Support and move the Skype folder to Trash. Then you need to delete supporting files of Skype in Library folder. Open Finder > Applications folder and choose Skype in the folder. Otherwise, you may be unable to move Skype to Trash because the app is still running. Here is how to uninstall Skype completely:
If your Skype tends to quit unexpectedly or get errors, it is a good to perform a clean uninstallation to give the app a fresh start.