If you need to save a part of an image, and you don’t want to resize your current canvas size, you can use “copy merge” functionality.
Make your selection with select tool (Press M). Now, from the top menu, continue as describe below:
Edit -> Copy Merged [Shift+Ctrl+C]
File -> New [Ctrl +N]
Photoshop should automatically suggest a new canvas size to match the selection size)
Edit -> Paste [Ctrl+V].
File -> Save As [Shift+Ctrl+S]
Rinse and repeat… ( keyboard shortcuts are handy here)