One of my grandmothers made all her quilts the same way. I've made a couple (usually with flannel). Here's how I do it:
Are you tying or quilting the quilt? If quilting, make sure to leave a little space (an inch or two) between your quilting stitches & the edge of the quilt. If tying, that pretty much happens anyway so no worries.
When it's all quilted or tied together, flip the backing back away from the edge as far as you can and trim the batting flush with the top of the quilt, DON'T cut the backing yet.
When the top and batting is all trimmed & square, flatten out the back and trim it down - I cut it down to about an inch & 1/2 because I like wider bindings on these types - basically I leave 2x the width I want extra. (So 1-1/2 inches of backing left gives me roughly a 3/4" wide binding)
Lop the corners off, leaving about 1/2" between your cut line and the corner of the top/batting. Fold that lopped-off corner down the rest of the way so the point of the top/batting is covered by the fold. Fold your binding edges over twice - first fold bring the edge of the backing over and butt it against the edge of the top/batting, then fold over again. Your corners should miter pretty much on their own. Pin (or glue) & sew!
The nice part is you don't need to worry about catching anything on the backside so you can focus on getting the top seam exactly where you want it. Don't forget to put a few stitches in the mitered corner so it can't come untucked.
OR you can skip the mitering and leave it all square and fold it over straight on all sides. That gives a thick corner that I'm not terribly fond of, BUT that's how my grandmother did all of her quilts and it works just fine.
