I don’t want anyone to use the extension that I have published anymore. I announced that I will be closing it down, but I’m afraid some people might have turned off updates to be able to circumvent my removal of the addon. Is there a way I can disable or remove the extension and make sure it’s uninstalled for all users?
You could release new version and call uninstallSelf:
But yes, users with updates disabled will be able to keep it.
If you don’t mind asking, why are you closing the shop?
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Thank you very much, but yea - I am not able to push more updates to people 
The reason:
The extension I had made had some improvements for an online forum-based community. The people using my extension have been very happy about it, and said it made the sitem uch better, but recently the management behind the website has made some serious changes that I don’t agree with. I want to remove the extension from everyone, because I don’t want to support people having a “better” experience on a website that I am so disappointed in.
I made the “error” of announcing that I would take down the extension before I actually did, and I think some people disabled the updates to NOT lose the extension sadly.
I will try to contact support and see if they can help me.
To address the title of the thread, no, deleting an add-on from AMO does not have any effect on existing installations of that add-on. The only way for you to try to remove the add-on from user devices is to use management.uninstallSelf() as suggested by @juraj.masiar, but even that is not guaranteed to work.
In addition to turning off updates, users may be on networks that block traffic with AMO servers, they can fork the extension, they could have Firefox policies that prevent the extension from accessing the management API, or there could be other factors that prevent your cleanup from being 100% effective.