I always use a spreadsheet!
While this is not what a spreadsheet is designed for, I find it really does work.
Open a new spreadsheet, and turn on page gridlines. In excel you can do this on the Page Layout tab and then tick and untick the "Gridlines: Print" section:
Next setup your page size. Mine defaults to A4 (210mm x 297mm) but your may default to 8.5" by 11" if that is a common size.
Now, insert the image. I chose a 121 MP image of earth to insert.
As you can see, it spans many pages. I now set the margins to narrow, as my printer can cope, and make it as big as I can within the 3x3 page limit. You may find changing the paper orientation to landscape will allow to you make the image slightly larger. This depends on page length ratios and image length ratios.
It's sensible now to print to a PDF, or a file, to check it looks okay.
If you want each image, upload the PDF to an image extract program - I like SmallPDF.
If you want it on paper, then check the edges will line up, and hit print!