How to to deal with advisor's criticism of my writing? I am about to finish my PhD, which means I have to write a lot. I am also a non-native English speaker, so my English sucks a lot, especially when it comes to formal writing. In contrast, my adviser is a very good writer and good writing is very important to him.

Whenever I write anything, from an e-mail that gets CCed or a draft or a paper, it attracts relentless criticism. I know that I am supposed to use this feedback to improve, but I am a bit tired of this “tough love.” 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.

I do try to improve my writing by reading a lot of high-quality English texts and practicing on my own. I took an online course on writing and developed my own writing routine: at first, I plan paragraphs and the flow between them, write a first crappy draft, then edit into something tangible during multiple rounds.

I also try to incorporate my adviser's guidance. However, my writing morale is currently so low that it stalls my productivity. 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 know many students lack feedback from their advisers, but I am just fed up with feedback. Is there any way to get out of this hole?
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.