You don't have to delete your local branch.
Simply delete your remote tracking branch:
git branch -d -r origin/<remote branch name>
(This will not delete the branch on the remote repo!)
See "Having a hard time understanding git-fetch"
there's no such concept of local tracking branches, only remote tracking branches. So origin/master is a remote tracking branch for master in the origin repo
As mentioned in Dobes Vandermeer's answer, you also need to reset the configuration associated to the local branch:
git config --unset branch.<branch>.remote
git config --unset branch.<branch>.merge
That will make any push/pull completely unaware of origin/.
Source: http://stackoverflow.com/questions/3046436/how-do-you-stop-tracking-a-remote-branch-in-git
Thanks, this was very helpful. ๐