there was a recent article in the NYTimes (june 16th of this year) about crossing spider genes with goats, in hopes that the goats milk would contain the proteins for the spider silk, with could then be extracted..

modern day nylon is spun out of spinnets, the ideas taken from how spider spin their silk

spider silk is stronger than steel.. so its not really too surprizing silk is strong as it is! spider silk, and real silk are extremely fine fillaments, but they have wonderful tensil strenght. and when spun into thread, and woven into yarn, they are extremely strong! but, they can be cut.. ( ok, if you take a filament of silk, and gently stretch it.. either by pulling on the ends, or by securing the ends, and pressing down on the middle, it is stronger than steel) but if you place a sharp edge against it, it cuts, very clean (almost perfect right angles when views through a microscope)
so an arrow striking the cloth, is like force like the first, hanging or pulling, it testing the tensile strenght, and the silk resist very effectively. but a scissor, is cutting.. modern arrow come with several different heads.. the classic arrow shape (flat blade, with beveled edges ) is sometimes sharp enought to cut the silk, but most often the silk reacts as if the arrow head were a series of steps, and each step is just pushing, putting presure on the threads.. and silk resist this presure very effectively.