Is there an easy way to clear/empty the clipboard?
To set a combination of keys to clear the clipboard, you can create a Service using Automator.

Your service will have a single action, Run Shell Script

The shell script you will use is this:

 pbcopy &lt;/dev/null




Then save the service and assign it a keystroke using System Preferences » Keyboard » Keyboard Shortcuts » Services.



The challenge of an application that automatically clears the clipboard one minute after the last paste operation is that said application would have to monitor all the copy and paste events across all applications; presumably you would want the action cancelled if you pasted and then copied new text (you wouldn't want to clear the new content from the clipboard one minute after the last paste of the previous clipboard contents). Such a program could be written, but implementing it with AppleScript or Automator would be a challenge.