Oh I would not do it, the selvage edge has no give to it. Your project will most likely buckle.
I snip the cut edge about a half inch from the selvage edge then grab and rip the fabric. It will rip in a straight line, if you don't plan on saving your selvage edges in some cute slevage project then save it anyway, its great (very strong) rope for tying things...like tomatoes in the garden, boxes for recycling etc. Best thing is you know that you have a perfectly straight edge.