How to make a paper anonymous for reviewers when it heavily extends on your own previous work?

Disclaimer: I work in a field in which double-blind reviewing is either completely absent or so rare that I have never encountered it.

Would it be acceptable that I mention that this paper extends my previous research that cannot be cited in order to accomplish the anonymity of a double-blind peer-review, and that the citation will be added later?

No, I don't see how that's possible. The principle that you must cite work that you use or build on -- no less so if it's yours -- seems much more basic than your desire to get genuinely double-blind refereeing. Moreover, if a paper continues previous work, can anyone sensibly evaluate its added value without having access to that previous work? I can't see how.

I am a new guy in the field, and I can imagine that this is where a reviewer could have prejudices. Stupid reason, but I already have an unpleasant experience with this.

When you self-identify your reasoning as "stupid", there's a clear opportunity to think it through again. The process of journal submission and publication has a non-negligible random component: it would be unwarranted to assume that an experience that you had once or twice will necessarily recur. Your desire to circumvent an unfair refereeing process seems premature. If you feel like you're being treated unfairly as a new researcher, there are more productive ways to react to this: make it more clear why your work is competitive with or superior to the work done by more established researchers. I don't know of any academic field in which journals systematically don't want to publish work by new researchers that they believe is better than prior work just because those researchers are new. It is also true, unfortunately, that new researchers can overestimate (and also underestimate!) the value of their work. It is hard to hear that the thing you slaved over for months and years is not good enough for a second-rate journal in your field. But it may be true nevertheless.

Let me say finally that I see a little irony in your approach: you lament your treatment as an unestablished researcher, but you are in fact more established than most people: you have published a paper that your present work builds on. My experience is that it is much easier to publish a second paper on the same topic in a reasonable journal than a first paper, just as it is easier for an artist to sell their second painting for a reasonable price than their first. In publishing the first paper, the journal has conferred on your work the important imprimatur of publishable value. Insisting on throwing that away will probably increase your chance of receiving "anti-newbie bias" in the evaluation of your followup work!

The standard practice in my field (i.e., psychology) where blind review is required is as follows:

Just cite your own previous work as if you were citing any other study that was not yours.

For example, if your name was Bob Smith and you published a study in 2015, and you are now writing a paper that builds on that study, you could write something like:

Smith (2015) recently extended research on X. The present study builds on the models proposed by Smith (2015) to ....

In a few other contexts, it can also be appropriate to black out some text with a note saying "hidden for purposes of blind review". I would not use this for references. But I have used it, for example, when I needed to state the specific university ethics board that reviewed a study.