If you in Preview select the half of the A3 (e.g. use the Inspector ⌘+I so you get the exact size) - then choose Copy ⌘+C, and paste it as a new file ⌘+N. After that do the same with the other half of the A3.

If you in Preview select the half of the A3 (e.g. use the Inspector ⌘+I so you get the exact size) - then choose Copy ⌘+C, and paste it as a new file ⌘+N (my suggestion would be to save each new file as its page number). After that do the same with the other half of the A3.

If you save every new file as its page number, then afterward you can select all the new files in Finder. Once they're all selected, right click and choose Quick Actions > Create PDF (available in macOS Mojave). You'll have a new PDF that is composed of every pdf you had selected.

If you in Preview select the half of the A3 (e.g. use the Inspector ⌘+I so you get the exact size) - then choose Crop ⌘+K, and print this "new" page e.g. as a PDF - after that you Undo the Crop with ⌘+Z, and do the same with the other half of the A3.

If you in Preview select the half of the A3 (e.g. use the Inspector ⌘+I so you get the exact size) - then choose Copy ⌘+C, and paste it as a new file ⌘+N. After that do the same with the other half of the A3.