When I tried to mirror the right side of the stomp walk to the left, I first deleted the left sides keyframes. To my surprise, when I hit the play button, the animation still ran as if I hadn't deleted any of the keys on the left side! I tried undoing and deleting them again from both the graph editor and dope sheet, but it had the same effect. How do I delete the keyframes on the left side to that when I play the animation, the left side stays still an only the right side moves?
Just make sure you are selecting all the controls you want to remove the animation from - and also make sure you are 'deleting' the animation.
By default the mouse will pop over the "clean keyframes" option when you hit x or delete.
(Cleaning the keyframes doesn't delete the animation, it just deletes the unnecessary keys)
If that doesn't solve your issue, can you post a video of the steps you are taking.