I wrote all this below, then realized it's probably wrong because of how I think the ruffle is constructed. The ruffle is made from a string that goes back and forth, say left to right, then right to left, on and on. You get the fringing in the method I wrote below if you cut perpendicular, up and down, to the direction of the knitting. If the direction of the knitting was along the edge of the ruffle, it won't fringe, only the outermost strings will come off, unraveling like Ceit suggests. Need a closeup picture of the ruffle to be sure.
<strike>Do you have a sewing machine? You could try something akin to steeking, which is how sleeves are put into the bodies of Nordic sweaters that are knit in a continuous s, although then you don't want the fabric to fray. With the sewing machine, stitch around the perimeter, really small stitches, a good 1/2" back from the edge or however long you want the fringe. Then use sharp scissors to cut the binding off, the first round of stitches closed to the hem. It will fray back to the edge, you'll probably have to help it and then trim it to even it up, as I guess some of the scallops will produce longer threads. If you were into lace, could stitch some lace down underneath the ruffle as you did the locking-down stitches, which would peak through the fringe. If you haven't worked with cutting knitted fabrics, I'd buy a super cheap knit at a thrift shop to practice on.</strike>