You can set a default action to hide this prompt from the Internet Options menu. Go to Tools > Internet Options, then open the Security Tab. You can set a default for either general Internet sites, Trusted sites or Restricted sites. For info on why you see this prompt, and why by default you should not allow clipboard access, see this MSDN article
If you want to allow access to your clipboard, add the site to your Trusted Sites (and make sure you actually trust the site, since allowing this option can allow them to copy clipboard info like passwords). If you want to just disable clipboard access by default, just pick Internet to automatically disable this option everywhere (it's quite rare that it will be requested).
Click the Custom Level button, then scroll down to the Scripting settings; you can set a default for Disable or Enable for Allow Programatic clipboard access.
Here I trust the site so I've added it to my Trusted Sites list and set a custom level only for Trusted Sites to allow this option. You can also disable this option if you don't trust the site or don't need the feature.