What can I do if I am constantly invited as a reviewer, but don't have the time? I've recently started as a PhD student, but had previous publications in forms of conference papers and various talks, so I consider myself very experienced with my particular field of research. One of my supervisors had once assigned me for a review task for a journal because she did not have time to complete it. This was fine with the editor of the journal, too.

Starting from that date, I began receiving invitations to review manuscripts every few months. Of course, I took that opportunity and completed the reviews – which naturally takes a lot of time.

Now, I cannot really invest the time anymore. I've previously rejected two review invitations with "I do not have the time to complete this review" (or similar), but I keep receiving invitations.

What could I do to politely ask the editor not to consider me for review?

Is there anything I'm about to do that could be considered inappropriate? I understand that reviewing activities are positive contributions to my academic career, but I don't think I can take it now.
As far as I know, there is no official please-do-not-bother-me-ever-again button that removes you from the reviewer list in a journal's submission system. That being said, I assume just writing the editor a polite email should do the trick. Other than that, you can always continue to refuse reviewer invitations, and I am pretty sure editors will relatively quickly stop sending you invites (they hate wasting their time, too).

That being said, I would personally urge you to reconsider your stance on this. Reviews are an important community service that are essential to the functioning of science, and one review every few months really is not an over-the-top amount. For instance, I review at the very least one journal submission every month, plus proceedings papers for conferences and workshops where I am in the Technical Program Committee. That you recently started your PhD studies should actually only be more of a motivation to keep reviewing, as this is actually a pretty good way to stay on top of your field.