1) Close the game
2) In their Steam Client, go to Steam->Settings->DOWNLOADS+CLOUD, and uncheck the box "Enable Steam Cloud synchronization for games which support it"
3) Go to C:\Program Files (x86)\Steam\userdata
4) Look in each of the folders and delete any subfolders named "219740"
5) Launch the game from Steam
6) Start a new game, and an error will popup "Failed to load the save game, as the file is corrupt"
7) Choose "Overwrite", and then "Yes" to confirm
8) Close the game
9) Re-enable the check box in Steam cloud settings
10) Launch the game from Steam, and a Steam warning will popup "Your local Don’t Starve files conflict with the ones stored in the Steam Cloud."
11) Choose "UPLOAD TO THE STEAM CLOUD"
12) Save data is now permanently cleared for Don’t Starve