How can I post my own version of a published SPIE paper on arXiv? SPIE policy for web posting of papers states the following:

SPIE grants to authors (and their employers) of papers, posters, and presentation recordings published in SPIE Proceedings or SPIE Journals on the SPIE Digital Library (hereinafter &quot;publications&quot;) the right to post an author-prepared version or an official version (preferred version) of the publication on an internal or external server controlled exclusively by the author/employer, provided that (a) such posting is noncommercial in nature and the publication is made available to users without charge; (b) an appropriate copyright notice and citation appear with the publication; and (c) a link to SPIE's official online version of the publication is provided using the item's DOI.
This authorization does not extend to third-party web sites not owned and maintained by the author/employer such as ResearchGate, Academia.edu, YouTube, etc.
SPIE content published under a Creative Commons CC-BY license is exempt from the above requirements.

Emphasis in the above text is mine.
So if I understand correctly, once the paper is accepted in SPIE (journal or proceedings) for publication, then I cannot post it on arXiv (since the arXiv server is neither exclusively controlled by me/my employer). I am talking about my own version, not the published one.
I tried to submit my own version on arXiv and they understandably rejected it saying that they cannot accept anything that has a journal copyright. So is there a way around it for me to submit my article to arXiv?
If not, I think I can surely post it on my own website, right? I will post the copyright and the DOI in that version.
So is there a way around it for me to submit my article to arXiv?


It's reasonable for you to ask SPIE for permission to post the paper to the arXiv (under conditions (a), (b), and (c)).  They might not grant permission, but it can't hurt to ask.  Even if they deny permission, at least you've given them feedback about what authors like you want.

One possibility is that they actively object to posting on the arXiv.  In that case, you are probably stuck.  Another possibility is that they don't specifically object to the arXiv, but don't want to authorize arbitrary websites they are unfamiliar with or other websites they object to.  In that case, they might grant you permission.  If they do, then that should suffice for the arXiv administrators.


  If not, I think I can surely post it on my own website, right?


Yes, assuming it is controlled exclusively by you or your employer.  (That's true for most people's websites, but it could fail in unusual cases, for example if you are treating a social network page as your home page.)