I just had to manipulate 4 1/2 yards into strips just today. I would do as tallchick suggests, but a couple of additions.
If you're worried about the bulk of the fabric, bi-fold it, it'll look like an accordion after you're finished. Don't let the bulk hang off of the side of your cutting area, that's where your cuts will become inaccurate because that weight is pulling on your fabric. Make sure it's lined up on your cutting mat and then start cutting. Measure twice, cut once - it's a mantra a lot of us use and it works like a charm.
Cut all your strips first, the majority of the cutting is actually there and once it's out of the way, the rest will be easy. Just take your time, make sure everything is lined up correctly. Once you get done with the strips, pile them up, then take a couple, line it up like you did the bulk and do your sub-cuts.