Hi @kreeg 
Welcome to the Canvas Community, and sorry to hear that you are having this issue! The bottom line is that this should not be happening within the DocViewer in SpeedGrader. Word-based documents should definitely be opening, as should many other document types as outlined here: What types of files can be previewed in Canvas? (Though note that the file must be under 100MB, which I imagine is the case for you unless students are doing something like embedding tons of JPGs in the file!) The fact that it icon just spins around, as you said, seems to imply that the Canvas DocViewer is trying to render it but ultimately failing. You said you could download them, however, and (I assume) have them open for you in Word. (But why re-save them as a PDF? You should be able to leave them in Word format and re-upload them to students....just as an FYI.)
If you can, you may want to reach out to a few of the students whose files were not opening and ask them how they are saving their files and what program they are using. Is there a common thread, perhaps? When this happens to my own faculty (and it will, on occasion), I suggest they just wait a while and do something else and then return and it usually works just fine; there are indeed the occasional slow times. But if this is consistently happening to you, it may be time to reach out to Canvas Support (Help>>Report a Problem), which may be first forwarded to your local support. And that may not be a bad idea....because if this is happening in more than one class, your local support will want to know about it, as well.
I hope this helps a bit, Kerry, even if it does not offer a solution.
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