As far as I can tell from the printer's description on the HP website, your printer doesn't have any built-in picture editing functions. (Some printers allow you to insert an SD card and edit images on a screen built into the printer, eliminating the need for a PC). So the only reason your printer is producing the wrong output must be that your computer is providing it with the wrong input.
I seem to recall that you're using a Chromebook, together with the online editor, Pixlr. For a simple task like cropping an image though you might just as well use the editing facility that's built into your Chromebook. (Double-click on your image file to open it in 'Gallery'. Then click the 'Edit' button in the bottom right-hand corner). That should avoid your current difficulties.
If you're determined to stick with Pixlr, make sure that you're using a 'Save' button within the window you're viewing and NOT the 'Save' function of your browser.