pretty straight forward-
Stack the layers flat on the floor. To secure, run a few basting stitch rows either width or lengthwise thru all layers.... a basting stitch will be a long running stitch about 3" or more in length. This will keep all layer togther better than stitching along the edge.
You can do this by hand w/ a sailing or leather needle (which is curved and has a sharp point) for cutting thru thick material (yoga mat = 1/4" thick). this can be done on a home sewing machine by changing settings, needle quality, foot pressure, and if the yoga mats stacked are thin..
See example below for ref.
Since this will secure all layers together you will be able to trim edge evenly and apply fabric shell/lining without too much pad slippage... set outershell and lining with straight stitch machine along edge 1/4" margin, set 1/2" width binding trim to edge with machine or iron-on adhesive (stitch witchery is your friend)

hope this sheds some lite, i can't turn off what i do for a living sometimes...