The first thing you should try is:
sudo pip uninstall pip
On many environments that doesn’t work. So given the lack of info on that problem, I ended up removing pip manually from /usr/local/bin.
In my case I ran the following command and it worked (not that I was expecting it to):
sudo pip uninstall pip
Which resulted in:
Uninstalling pip-6.1.1:
/Library/Python/2.7/site-packages/pip-6.1.1.dist-info/DESCRIPTION.rst
/Library/Python/2.7/site-packages/pip-6.1.1.dist-info/METADATA
/Library/Python/2.7/site-packages/pip-6.1.1.dist-info/RECORD
…
/usr/local/bin/pip
/usr/local/bin/pip2
/usr/local/bin/pip2.7
Proceed (y/n)? y
Successfully uninstalled pip-6.1.1