I mark the cutting edge with a permanent Sharpie first, then sew around the edge close to the marked line, either a little inside or a little outside the marked line. I do *not* trim before attaching binding; I attach binding for the first side using the marked line to line up the raw edge of the binding. Only after attaching the binding do I finally trim the edges, being *very* careful not to nick any of the binding fabric (especially at the corners).
Waiting to trim allows me to adjust the width of the sandwich in the binding to make sure it will will the binding the way I like it. Also, then I don't have to deal with cut edges of the quilt sandwich rippling or getting ragged from handling.
I noticed that when I cut first and then stitched around the edge, I was still likely to get some sliding, distortion and tucks because the sewing line is *so* close to the edge. The way I do it, just marking the cutting line without cutting, makes the edge much more stable while I work with it.