Sharper scissors. The ones I use are small, but very sharp. I only have to start a cut, then I can just push them through the material the rest of the way. Really loose woven burlap bunches up sometimes doing this, but still cuts really easy when I close the scissors on it.
I use kinda thick burlap the kind coffee beans are in and tress for landscapers. I can get them really cheap. But it sounds like I might just need to suck it up...aaargh.. haven't tried the razor blade but might give it a go...
Try bandage scissors (EMT scissors). I haven't tried them on burlap but they are great for cutting just about anything. Even good for opening up those plastic clamshells. Saw a guy on youtube cut a thick towel with them. http://www.youtube.com/watch?v=cAw0P9z6A10
The way I was taught to cut that type of fabric was to get the length figured out and then pick one strand and pull it out of the weave to form a channel and then cut along the channel, if that makes sense to you. I never had any trouble cutting it that way with fabric scissors.
First get a board and put it down where you will be doing the cutting to protect the table. I also use a utility knife to cut with, the secret is to use a solid steel ruler held down tight and slide your blade along the steel ruler, or a piece of straight steel , maybe 1/8 of an inch thick or thicker, or use a square, same thing.
You could also use some kind of clamps to hold down the ruler , material and the board all at the same time.
The extra time and effort to gather up these simple things I have mentioned makes it So Much Easier and much more accurate cutting too along with less potential for cutting your own precious fingers.