As far as I know OSX doesn't have a clipboard history. Whatever you most recently copied is available for pasting.
There are third party utilities that allow for multiple clipboards and histories, but not OSX.
Also there's multiple undo but I don't think there's any way to clear that in the processes that support such a feature.
Actually... Yes it does have a history. The UndoManager maintains that.
Here is an except from a book which I read some time back:
Prior to Mac OS X 10.6, the pasteboard APIs allowed for only one item on the pasteboard at any one time (although that item could have an arbitrary number of representations, or types). In 10.6, Apple updated the pasteboard APIs to allow for multiple items on a pasteboard: for example, multiple URLs copied from Finder. Each item can have multiple types associated with it, such as string and URL representations.
Two examples of revealing this are:
1) In finder, click on EDIT -> Show Clipboard
2) Download an app which does this i.e. traverses through the historical items e.g. 'Flycut' which is on the AppStore
Flycut itself has an option to clear the clipboard history....