Storm doors are constructed of various materials, including wood, plastic, and aluminum.
Your ability to cut the door for height depends upon the material and the style of door. A storm door that is primarily glass will probably not be able to be cut down. It is possible to cut down a storm door made of wood, but other types are usually prohibitively difficult to modify.
It may be preferable to modify the door frame rather than cutting down the door itself. You can install a Z-bar extender to fill the gap between the door and frame.
If your door does not fit and you are unable to cut it down, consider ordering a custom sized door.