If you have Word 2000 or above, the easiest way to do this is to select "2
pages per sheet" in the Page Layout dialog (in Word 2002 and 2003, it's
under "Multiple pages" on the Margins tab). This creates two logical
portrait pages on a physical landscape sheet. You can either type the poems
continuously, two different ones on each sheet, or you can copy paste a
single one twice, or you can print each "page" twice by entering 1,1,2,2,
etc. in the "Pages" box in the Print dialog.

If you have Word 97 or earlier,  you'll have to accomplish the same thing
manually by dividing a landscape page into two columns. Make the space
between columns equal to the sum of your left and right margins.

There's really no need to cut the pages if you type the poems continuously
(so that you have two different ones on each sheet), and if you have Word
2002 or above, you could even create a booklet of them by using "Book fold"
instead of "2 pages per sheet."