I know I can edit My Vocab list by pressing the trash icon next to each entry, but is there a way to clear the entire list with one (or two) clicks? 

I don't think there is quick way to clear my vocab. However customer service did for a while ago when I wanted to change how I used it.

It would be nice to have a way of doing it ourselves.

Thank you for confirming. I've started clearing My Vocab out manually. I would have liked a one-click solution, but I also see the danger of that. If they were to give us the means of doing it ourselves, they should probably add a second step for safety, or an "undo" button.