After trying several different methods and ruling out the purchase of yet ANOTHER specialized tool to clutter up my house, I use the following method to remove those stupid clips very easily with a cardboard box and needlenose pliers:
A cardboard box slightly bigger than a shoebox is perfect. This method flicks the clip a few feet across the room if you don't contain it, and the box is a perfect way to keep it contained.
1) Put box on the ground, open end up. Put the stick down on its side, inside the box. Rotate the stick so the OPEN end of the E-clip faces up. Now go get the pliers.
2) Hold the stick down with one hand, using light downward pressure. It should rest with the handle touching the bottom of the box and the electrical connections tilted up in the air. With the other hand, hold the pliers facing downward, so the tip of each jaw of the pliers is touching one end of the E-clip.
3) Apply light downward pressure with the pliers, and it will shove the clip right off the stick. It takes a small amount of practice to prevent the clip and joystick from rotating out from under the pliers, but I mastered it in three tries and I'm not a ninja.
4) The clip probably will hop a few inches after popping off the bottom of the stick, but it will stay in the box. Pick it up, loudly curse the name of the sick sadist who invented, it, and then put it away for later reassembly.
Then go get a beer (optional).