You can also use git stash save -p "my commit message". This way you can select which hunks should be added to stash, whole files can be selected as well.

You'll be prompted with a few actions for each hunk:

y - stash this hunk
   n - do not stash this hunk
   q - quit; do not stash this hunk or any of the remaining ones
   a - stash this hunk and all later hunks in the file
   d - do not stash this hunk or any of the later hunks in the file
   g - select a hunk to go to
   / - search for a hunk matching the given regex
   j - leave this hunk undecided, see next undecided hunk
   J - leave this hunk undecided, see next hunk
   k - leave this hunk undecided, see previous undecided hunk
   K - leave this hunk undecided, see previous hunk
   s - split the current hunk into smaller hunks
   e - manually edit the current hunk
   ? - print help