| Ever seen the counter at a bar or restaurant where someone put down pennies and covred it in something to make a hard but clear coating? It might be a urethane of some sort. I would go to Lowes and check the clear finishes. You want something pourable. Another idea is to use a clear silicone caulk to just adhere the tile to the mirror top, do not fill in the cracks and instead cover the whole thing with a sheet of glass or plexiglass. You could get a piece of tempered glass from a glass shop if this was nice enough to be a table of some sort. I made this tile table - much different, but now I do know how fun it is to work with tile. The finished product can really turn out amazing! 
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