You can't do more things simply by going fast. All the things you are doing have to go along with you and move through time at the same rate as you do.
Suppose you accelerate to close to the speed of light (as seen from Earth), together with all the necessary stuff for doing the things you want to do. From Earth, it appears as if your wristwatch has almost stopped. You and all the stuff that goes along with you seem to move real slow. But you don't experience anything strange. It would be strange if all the stuff you brought along would move slower according to you. In that case, you could manipulate even less stuff (in reality, this only occurs if the stuff is moving fast relative to you, so you can't actually manipulate it).
If the stuff moves faster in time relative to you (which in reality never occurs), you would have a chance. You could make a sandwich in a flash (but eat it in your own time), travel to the other side of the Earth in no time, or wrap a packet in a second. But it would be very difficult for your body to synchronize with the stuff surrounding you. This would be a nice idea for a sci-fi movie.
Suppose you move away from Earth at near light speed with a huge amount of stuff to do. If you return to Earth, then, according to the [twin paradox] 1 things on Earth will have aged much more than you (and the stuff you brought along). So in effect, you'll have done the things you wanted to do in more Earth time. I.e., you'll have the same things in more time and not in less.
You could do things on a high mountain. Up there time goes faster than at sea level. Or even better, hire a rocket and do your stuff on board when circling the Earth. If you come back things on Earth will be somewhat younger than you and you'll have done more things than you would have done if you'd stayed on Earth. The amount of gained time is such small though that you better could have stayed down. It takes a lot more time to climb a mountain or take off in a rocket.
So it's best to just do things faster (and getting tired).