Another way to come up with a new mechanic is by asking yourself how things can be done differently. Thinking out of the box is a crucial skill for every game designer. What if is a great question to start with something you know or are familiar with and completely re-invent it.
A question like "What if we introduce zero-gravity in Super Mario?" can open an ocean of new possibilities and unexplored mechanics and gameplay. When trying to innovate, the less is more principle comes in handy again. Many games have innovated entire genres by taking out something from existing games.
"What if in a platform game the character automatically runs in only one direction and the only action available to the player is jumping?" ...
