You can set a default action to hide this prompt from the Internet Options menu. Go to menu Tools → Internet Options, and then open the Security tab. You can set a default for either general Internet sites, Trusted sites or Restricted sites. For information 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 information, 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 and then scroll down to the Scripting settings; you can set a default for Disable or Enable for Allow Programmatic 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.