All unnamed cloud objects can be deleted from a notebook (I assume that you want to do this from your desktop) easily:

DeleteFile[CloudObjects[None]]

I do this periodically, and this reminds me that I should save "important" cloud objects as named objects. For example:

CloudDeploy[APIFunction["x"->"Integer",FactorInteger[#x]&,CloudObject["myFactorIntegerAPI"]]

where "myFactorIntegerAPI" is the name of the file in the cloud.

For named objects, I don't know of a simple way to manage files from desktop notebooks. So I go to the cloud and open a notebook. Functions like SetDirectory["whatever directory"] and DeleteDirectory[Directory[],DeleteContents->True] work in the cloud.