When I'm working with wide backing fabric, I tear.
If it's a pieced backing from a customer, and I don't know that all of the pieces are on grain, then I have to cut. What I do is take one edge that is fairly straight and drape it over the rails of my longarm. Bring the opposite side up to meet the first edge (the fold is now hanging down near the floor). Move that second edge left or right as needed until the fold is hanging straight with no pulls or bulges. Don't worry if the left and right edges are aligned or not, those are the ones you will be trimming.
Now bring the fold up to align with the edges that are draped on the longarm rail. Again move left or right so the newly formed fold is hanging straight. You should now be able to take this piece to your cutting table and square off the right and left edges. Use the folded edge (with no raw edges showing) as a guide and cut the sides off at a 90 degree angle.
If the top and bottom edges also need trimming, you will need to open up the piece and repeat, this time using your newly straightened edges along the rails.
It does make it easier if you have a helper to do this, but I know from experience that it CAN be done alone!!
Andi