Welcome Betsy!! That's a great looking pattern you selected. I would probably cut one color at a time (like all the yellow squares). Since you need 2 of the white rectangles per block, that would keep you from having to cut all those rectangles at once. Another way to do it is to cut a 6.5" strip like Trif said, and cut all the 3.5" strips you can from that one strip and make a set of blocks, then cut another strip and make another set of blocks.
I do my cutting in a bit of an assembly line. For a color, I would cut all the 6.5" strips/blocks for one color block and then cut the the 3.5" size. The reason is I would place a piece of blue painters tape down the length of the ruler to mark the 6.5" (I have a ruler that is 8" wide) or 3.5" width (I indicate the edge of the tape to use as a guide with an arrow since I have been known to let my mind wander when cutting). That way you can see where to line up the cut edge easily (and nothing is as frustrating as cutting the wrong width and messing up a strip of fabric).
Have fun -- can't wait to see how you do!