I want to completely purge the old data that Skyrim stored in Steam Cloud, without replacing it with any new data (in other words, I just want to delete it). Is there any way to do it?

Thanks in advance for the replies

I don't know if you can delete things off of the cloud, but you can keep the game from syncing to it by going to your library, right clicking on Skyrim, picking "properties", selecting the "updates" tab, and then unchecking the "Enable cloud synchronization for The Elder Scrolls V: Skyrim".

Ok, this is not as obvious as it is with other cloud games. For instance, other steam cloud supported games you simply need to delete the folder on your computer that contains your saves and the next time the games syncs, the saves will delete as well. Skyrim is different in this regard. In order to properly delete game saves from the cloud, you must go into the game and manually delete each game save and once you're done, then exit the game. It'll sync and thus erase any data on the cloud as well. It's very strange, I know. It's also the only steam game I own, and I own quite a few, that requires you to be in game and manually delete the saves to remove them from the cloud. Anyway, there it is and I hope this helps.