Apple - Dividing PDFs on a Mac
Make sure your Sidebar tray is showing thumbnails (here's the icon to turn it on if it is not):
Select (highlight) your selection in the Sidebar tray (tricks for multiple pages - 1. if they are consecutive you can click the first, hold down shift & click the last to select the range; 2. if they are NOT consecutive you can hold the command key while selecting the pages you want)
Copy (here's the menu selection, you can also command+C)
You will note in the File Menu that the choice for New has changed to New From Clipboard - select that to create a new document from your selection
Make sure to save it!
If you are like me and whittling down a huge document, you can then deleted the pages you "extracted" out so that the document only has pages left you have not worked with yet.