Buy a mirror in the size that you want to mount. You can cut mirror, but the endeavor requires precision and many tools. You can buy mirror from a local dealer.
Buy plywood the same size as the mirror. Your local hardware store can cut the wood to your desired size. Be sure to take measurements so you get an exact fit.
Cover the floor in a well-ventilated area with a large blanket. The blanket will catch falling glue or splinters from the plywood so that the surface underneath stays clean.
Place the plywood flat on the blanket, and cover the surface with wood glue. Run the adhesive tube in lines up and down the wood surface, making sure to apply a line close the edge so that the mirror sticks to the entire piece of wood.
Place the mirror on top of the plywood, and gently press down over the entire surface so that the mirror grips the glue and sticks to the wood underneath. Place small clamps around the edge of your plywood-backed mirror so that the two stick together while drying.
Wipe any excess glue away from the edges with water and a washcloth before it dries.
Let the glue on your plywood mirror dry for a full 24 hours.