Glue on your pieces with Locktite power grip then grout as you would tile.
A successful exterior application of mirrors will be dependent on the substrate being water proof Or at least weather proof.
For example, cedar fencing or vinyl fencing.
Pine will not hold up.
In addition to Cheryl's advice, the mirrors will be subject to breaking from temp changes, wind, etc. and if water gets behind them the silvering will come off making them just panes of glass.