I usually add to index changes I don't want to stash and then stash with --keep-index
option.
git add app/controllers/cart_controller.php
git stash --keep-index
git reset
Last step is optional, but usually you want it. It removes changes from index.
Warning
As noted in the comments, this puts everything into the stash, both staged and unstaged. The --keep-index
just leaves the index alone after the stash is done. This can cause merge conflicts when you later pop the stash.