It is hard to fold and cut fabrics strips that long. I usually use my chalk pump pencil and my square and draw a line all along the selvage edges the amount (plus the selvage and a little extra) I need. I then pin the two layers together to keep them from moving as I use my scissors to cut along the line. This gets the fabric down to a more manageable size. I then fold the cut off pieces as many times as needed to fit my large mat. Once the fabric is folded, I use my square and ruler to trim off the salvages and cut the strips needed.
I do not think you will have much luck tearing off the border strips with batiks. They are dense and even if you do get them to tear, I think you will still have to trim the ripplely, stretched raw edges again.