How to to deal with advisor's criticism of my writing?

This doesn't answer your question, but I think your real problem isn't your writing, but the way how you and your advisor communicate. What I suggest is that you have a sit-down with your advisor and raise the issue with them. Tell them what you told us - that their barrage of negative feedback is hampering your motivation and productivity, and that you would have an easier time incorporating their feedback if they could find a more positive way to phrase it.

Of course there is no guarantee that this conversation will go over well (some people think that "tough love" is the only way to give feedback, and others understand on a rational level that a more "sandwich" style of feedback works better for most people but are unable to change). However, you will never know if you don't raise the issue with your advisor.

Edit: to say a little bit about "writing better", the actual topic of your question -

You should also try to understand if your advisor is really dissatisfied with the mechanical aspects of your writing (spelling, expressions, grammar, paragraph construction) or with your skills in scientific storytelling. It seems to me that basic command of the English language is not a real issue for you, so potentially what your advisor is actually dissatisfied with is that you do not know the terminology of your field well enough, common rhetorical moves in your discipline, how people like to construct arguments, etc. If this is your problem, a general-purpose writing course is not going to help - you will need to study papers in your discipline to improve.

I often get desperate and anxious because I feel I can’t write anything worthy at all. It causes severe writing blocks because whenever I am about to write a sentence, I immediately imagine it being totally destroyed and thrown into a garbage bin.

Your writing course is giving you the correct guidance here. Good writing is mostly about clarity and good editing, so it is not terribly important that one's initial sentences be of good quality. When you are writing academic work, it is best just to get your thoughts down on paper in the first instance, to express the substance of your ideas and their logical connection. Once you have some material down on paper, you can edit and polish as much as you like to improve the clarity, structure and prose. The most important thing is to edit to make sure your writing is clear, and does not tax the reader. If you are having difficulty with structure then it is useful to work from an outline, and to create a reverse-outline from your written work to check that it follows the structure you intended.

Developing good prose is more difficult, but the best way to do this is to read material by good writers and then analyse why you found their writing so compelling. Make sure you do not confine yourself only to reading academic papers; read novels, other prose pieces, and even good journalistic works. When you read good writers, over time you will begin to pick up techniques they use to make their writing clear, compelling, and powerful, and you will also expand your vocabulary. This will allow you to improve your own writing and develop your own style.

I do try to not take my adviser's criticism personally, which is quite difficult sometimes, but I am just so tired of being judged all the time.

I guess this is the nature of being in an educational program, even as a higher-degree student in a PhD program. These kinds of programs generally entail non-stop judgment of your work and critical feedback, with the goal of having you gradually improve. It is important to balance judgment and critique of work with occasional morale boosters, so it may be time for you to take a break and look back on all the things that you have already accomplished. If you are feeling burned out by all the criticism, talk with your supervisor and see if it is okay for you to take a break from your program to take stock of your existing work and accomplishments, and give you time to boost your morale.

I am in the same boat. Trying to get my PhD Thesis written currently.

To add to all the great advice from others: Try also to read the papers/project proposals and other text you wrote in the beginning of your PhD, and compare them to what you wrote now. This really helped me a lot to see how my writing (non-english native as well) developed over the course of my PhD. I am sure yours has developed too!

What also helped me is to note down/realize my most common mistakes and then when proofreading specifically check for those. For me usually it is using "that" in all places where it is unnecessary. While proofreading I do one run just paying attention to that one mistake.

And in addition: Do you have friends/family/colleagues or even english natives willing to proofread? Even if they do not understand your Topic they could give you feedback on your language. So you can send your advisor a first draft where you already polished the language a bit.

But generally keep your workflow up! Writing a draft and polishing it is the best strategy to get something done. Polishing is always easier than writing the perfect sentence in the first place.