Q&A: Supersize Cut-and-Paste in Microsoft Word, NYT article.
While the basic cut-and-paste maneuver just grabs one chunk of contiguous text from a file at a time, recent versions of Microsoft Word include a helpful feature called the Spike that may help here. The Spike is sort of a longer-term storage area within Word. By using the Spike, you can select and cut noncontiguous text from around the original document — and then paste it all as one big batch into the new file.
This is great.
Except: note the little word "cut"... the text and images are not copied, they are cut. They disappear from the document. What an odd choice in programming.