How to exclude an item from a view if it appears in another view on the same page?
So you have 2 views: "Promoted News", and "Latest News" View.

To exclude any view results ('items' as you call them) from "Latest News", add a 'filter' in that view with as criteria the opposite (negation) of the 'filter' criteria that are used in your "Promoted News" views.

E.g. if "Promoted News" is implemented with a filter like "published to frontpage", then in "Latest News" the filter o be added should be "NOT promoted to frontpage".

Note: If you're new to Drupal, you might also want to review the set of 30 video tutorials about the Views module to become more familiar with the Views module.