This doesn't currently seem to be a feature available in CiviCRM, however, when setting up the schedule reminder, there is an option to "Record activity for automated email or SMS" - if this is toggled, then you can set up an activities dashlet on your dashboard filtered on the given activity such that every time you login to the back office you will see if any reminders have been sent - this option might even be preferable to receiving an an email and will definitely keep your inbox more manageable).
Hope this helps!
Tamar