How to have different game data profiles in Skylander?

The character progress is stored on the figures themselves, no matter what platform or save you play them on, that's the main feature of the game.

You can have different saves, but they only have the game progress and unlocked hats.

If you wish to have a fresh character, you can either use a new figure or reset an existing figure's progress through the character menu (select on PS3, back on x360), please note, however, that once you reset a character, it is reset for everyone using it.

All Skylanders have their stuff stored on the figure. You can get multiple figures of the same Skylander and mark whose is whose.