Place the water, 1/2 sugar, and mint in a small pan and bring to a simmer, stirring occasionally to help dissolve the sugar. Let simmer over low heat to steep the mint. Then strain the mint from the simple syrup. Discard the mint.
In a food processor combine 2 cups of strawberries with the remaining 1 tablespoon of sugar. Run the machine to puree the strawberries. Add the mascarpone cheese, lemon juice, and salt. Run the machine until the mascarpone cheese is fully incorporated. Add the mint simple syrup and run the machine to combine. Place the strawberry mixture in an 8 by 8-inch glass dish and place the dish in the freezer. The mixture will take about 4 hours to freeze.
To serve, use a fork to scrape the granita. Spoon the mixture into chilled bowls. Top with the finely chopped strawberries. Serve immediately.