"How does one clear one's mind to begin writing?"
Dear Reader, thank you for sending me this question.
I look at writing from a different point of view. What I clear is my writing table, not my mind.
I move everything off the table except the paper I'm using, if it's a paper and pen thing I'm doing. I place the pen on the paper and begin writing.
It's a Natalie Goldberg technique. Keep the pen on the paper and keep it moving no matter what for ten or fifteen minutes. It doesn't matter what you write. The only guideline is, "keep the pen moving: do not take it off the paper."
This also addresses another part of your question in which you said that it takes ten or fifteen minutes of writing to get out the stuff that you consider in your way. Let that be and just write.
You can make up your own prompt if it's easier for you to write in response to something, or just let whatever is in you come out. When you've finished with that read it aloud. See if there's anything in there you like.
Place another clean sheet of paper down and begin what you want or continue with another pen on paper exercise.
Looking at the image below you see that there's all manner of things inside us waiting to be expressed. All part of us. We tune in, letting it come forth and organize it.
This is a partial photo of a piece of art by John Balloue, a tribal member of the Western Band of Oklahoma Cherokee. The title is "Survivor."
I think is demonstrates the richness, the infinite experiences and connections we all have.
So, here you have a portrait of yourself, dear reader.
Go to it! Expand andnjoy