Mindless doing is the exercise of executing a task by shutting the mind as you continue!
Isn't that ridiculous? How can you keep doing without thinking?
The mind is like a geared wheel. If you try to let it run on its own, it adapts to where its inertia leads it. Be keen to notice this and you will feel it does!
This is extremely important when you want to focus on a task.
Example, if you are mastering to play a musical piece, you do it in repetition. Do it again and again, slowly, until your hands tend to get its own pace. You will feel that your mind is detached from it. It's a pain at first until you get sort of numb from it. Try to enjoy the numbness of the process. After a longer period of doing, stop a bit. Drink water. Shake your hands and start again. Do this in several days in between longer rest and intense focus.
Be a living factory within yourself. Do it the blue collar way. Work something out by doing it repetitively in the most mindless way you can. Don't get me wrong, the mind is processing it. You just don't have to tire it by over-thinking.
Do without thinking too much. It is more productive than procrastinating. Seat down at once and just do! The mind has many ways of accomplishing tasks. This non-trivial method is one of them.