When I cut a border print, I usually cut it along the straight grain (along the selvage edge) of the yardage. Using a short ruler like my 6" x 12" I carefully slide it along the design, cutting as I go. It takes longer than folding the fabric, but assures a straighter-on-design strip. I place a pin at the 84" mark to know where to stop.
If I have to cut on the cross grain (from selvage to selvage), I still cut one layer at a time as above. When I join the strips to create the length I need, I try to match the design -- you often lose a bit of fabric here -- by drawing a line across the design on the strips I have to join so that the pattern matches when I sew.
Jan in VA