This is one of five panels I've been commissioned to do for the outside of a live-work loft in Bellflower, CA. I'm now working on the second one which is of the town's clock tower.
Get yourself one of those handy under-the-bed-sized plastic storage tubs or whatever will fit the pieces of mosaic the way you've sized them. Lay down some plastic sheeting in the tub cut to size, and gently lift your mosaic-on-mesh piece up to see that all of the pieces are in fact adhered. If any pieces come loose or were never actually glued, then simply lay the piece back down and glue the piece back on. When the glue is dry and all the pieces are secure, lift the mesh-mosaic sheet up, and gently place it in the plastic tub face up. Lay a sheet of plastic over that and continue to layer each sheet of tile with plastic in between. Believe it or not, I fit my entire 5' x 6' downtown mosaic into the tub shown here. I packed plastic bags into any free spaces, slapped the lid on, and I'm on to the next mosaic panel!
Once I cut all of the mosaic into pieces, I labeled each one using 3" x 5" index cards and low-adhesive painters tape. I labeled them from left to right and top to bottom so the installer will have a clear idea of which piece goes where.
Once your mosaic is finished and the glue has dried, cut along the previously established guidelines (Sharpie lines) so that your mosaic is a bunch of large puzzle pieces. Each piece should lift easily off the plastic.