You can use wp_schedule_event( int $timestamp, string $recurrence, string $hook, array $args = array() ) function to automatically remove the tag. This function will run automatically after the given interval. You can set the interval daily.
Daily the function will run and remove the tag from the post if current date is equal to certain date. You can also run it on hourly bases.
Please note that you have to write you function on the hook of schedule event that will check the date and remove the tag.