All the blackout poetry I have seen takes a black marker and literally blacks out everything but a few chosen words that appear in what looks like a haphazard order.
I do not black out. I select. And, then I put the selected words into the lines of a poem. The words stay in their original order, but I decide the line breaks and punctuation.
It's a good thing that I don't black out because I revise extensively until I feel the poem is as good as it can be giving the restrictions of the form. If the words were blacked out, I wouldn't be able to put them back in.
For example today, as I wrote "Reservoir Wars, I noticed that a few words were rhyming. So I searched the news story and edited the poem to capitalize on the rhymes the reporter had inadvertently put into the news story.