I am an admirer of hand-cut collages, however, nowadays this technique is less used by artists as many prefer to crop images via Photoshop. An example is Joseba Elorza who does a great job at digitally composing pictures to give an old-school collage appearance. You can see the making of one of his photomontages at the bottom of the page.
Images © Joseba Elorza Via Svech