WHAT ARE MY OPTIONS IF I CUT THE DECK TILE IN A WAY THAT REMOVES THE SCREWS, SEPARATING THE TILE FROM THE MESH FOUNDATION?

Ideally, you would not want to cut the deck tile in this way as there is no definitive solution for attaching the slats back to the frame without the screws. You may try using Liquid Nails to adhere the frame and the tile. You may also use a c-clamp or wire clamp to attach the two pieces. However, we recognize that neither is an ideal solution and, in such cases, may be better to use a spare tile and cut it in a way that keeps the screw intact.