Mosaic Tile Bistro table
Then if you are going to leve the piece out side I'd ask a few painters what they think would be the best to seal the top with...
...perhaps an acrylic based grout may be enough, (if you remove all of the existing & regrout) but that may be a large job without the proper tools.
Then if the wood below the tile is beyond repair you may need to toos that puppy or trnsfer all of the tile to a new substrate. That will have to be your call? Does the wood feel punky under the tiles?