Clarifying email instructions with advisor I receive sometimes one line instructions from my PhD supervisor on work I need to do and send. Not always clear though. 

He sometimes forgets what he had discussed in our last discussion, or does not explain the rationale. Under such circumstances, how do I communicate with him? Redoing done work is I believe a waste of time and energy.
I think you should realize that your advisor is just an overworked human being. He tends to forget things, particularly what you, or other people in the group do because there are just too many things to juggle. It might be that he isn't a great planner and doesn't keep tabs on everyone in the group, but not necessarily. 

That being said, imagine you had to do his job. What would your student ideally do to make your life easier and still do good research? I'm not sure about you, but my ideal student would show as much initiative as possible. They would also self-manage themselves. If I ask them to do some work, they would know why I need that work done (preferably from our discussions), how does that fit in their, or our project and would try to do it on time. If they can't do it, for whatever reason, they would let me know as soon as they can so I can think of an alternative.

I personally don't forget what work I assigned, but if I do, I expect my student to remind me that, and the reason I asked for it. No need to redo work. You keep it short, something like: 


  Dr. [insert dude's name], I have finished the assignment you asked and sent you an email on [date]. I have attached it again. Regards, 


As for you not knowing the rationale for a specific task you get, I think you should try to find out from him when you discuss. Face to face conversation is very valuable because it's easier for him to make himself understood. It's also easier for you to get your information if you are nice and polite.