This bothered me as I quite often would close excel after pasting large amounts of data into their destination.
Best solution I found was a VBA Excel XLAM Addin that disables the clipboard on close. The only caveot with this method is if you close Excel your clipboard will be cleared.
Create an event for "BeforeClose" with the following then save as addin.xlam and place in your XLSTART folder.
Or you can download the one linked above.