I know I'm in the minority on this, but I have to say I hate controller vibration. When I bought the Xbox One instead of the PS4 (yeah yeah), I was surprised to find that there was no global setting to turn off this "feature." This was something that was available on the 360, so it was surprising that it was missing on the new console. It turned out not to be an issue since the first game I played, AC4, had a setting in its own menus to turn it off.
Then came Ryse: Son of Rome. No option to turn off vibration. Every step, every button push produced the annoying shaking. So what could I do? I checked all kinds of forums and found others with the same issue, though they were more concerned with their battery life. No way to turn it off, and no one in charge apparently noticing the requests in the forums.
I decided to do something drastic.
There are only two tools needed here: a Swiss Army knife with a can opener, and a pair of wire cutters. Yes, wire cutters. This is going to be permanent. Optionally, you should also have some small pieces of electrical tape.
Open the Controller
Using the can opener's very small screwdriver head, pop the seam around both handles of the controller, they should come right off. Set aside.
Find and expose the wires
There are two pairs of wires on either side of the controller. One pair is red and black, the other grey and black. One pair goes to the trigger vibration motor, the other to the main controller vibration motor. I don't know which is which, and it doesn't matter. They are both going down. Use the can opener to hook the wire pairs and pull them out where you can get at them with your trusty wire cutters. They won't pull out far, but far enough. If you yank too hard and they break off the circuit board, you can skip the next step.
You should now be able to cut the wires with the wire cutter. No going back now. Repeat on the other side of the controller.
Optional: Cover wire ends with electrical tape
I did this, but I don't think is is required. Use a small piece of electrical tape to cover the ends of the wires just to avoid any future short circuits. I think it's a good idea. Push the wires back into the gap so the covers can go back on.
Replace controller handles
Snap back on the controller handles, if you were a little too forceful removing them, you may have to smooth out some roughed up plastic around the seams.
Enjoy the vibration-free goodness
That was a piece of cake, right? The controller worked fine afterwards for me, though I only did this once and your mileage may vary, please don't come crying if somehow your controller gets ruined! Who knows, maybe someday Microsoft will fix this with a software update. Until then, break out your wire cutters and void some warranties.