I cropped an SVG in Inkscape and saved it (using this: http://goinkscape.com/how-to-crop-an-image-in-inkscape/).

In a browser it shows correctly, but when I try to import the cropped SVG into a publishing program, it shows the entire original file.

How do I save only the cropped image?

Here's the image I'm trying to save: https://www.dropbox.com/s/zuu7jtewwukf5 ... 1.svg?dl=0

Since all the objects are vector, I'd ungroup all, delete the parts I don't need, and use path operations on the staff lines to make them short. Then select all and resize page to selected.