How did you add the third-party software source originally? Reverse the process.
If the GUI tools aren't working then you can always edit the text files directly, using your favorite text editor. For example (using my preferred 'gedit' editor):
gksu gedit /etc/apt/sources.list
I suggest you read the linked document in #2 before
you edit these important system files. When I used to hang out on Ubuntu Forums, the #1 preventable cause of users breaking their systems was installing unsupported third-party software without understanding these basics. For example it appears from your kernel version that you are using Mint 13, is that correct? If so, you have added an incompatible
software source for "raring" (which is equivalent to Mint 15; it would be like trying to install Window 8 specific software in Vista). Adding software for the wrong release is a sure-fire way to get apt-get errors.