For the salsa: In a bowl, combine the avocado, mango, pineapple, red onion, bell pepper, cilantro, lime juice, jalapeno, garlic and a pinch of salt. Gently fold to combine. Adjust the seasoning to taste. Let sit for 30 minutes before serving, to allow the flavors to blend. (Makes 2 cups.)
For the mustard sauce: Combine the mayonnaise, dry mustard, lemon juice, Worcestershire and hot sauce in a bowl. Whisk well. Season to taste with salt and cayenne. Thin to a sauce-like consistency with heavy cream. (Makes 1 1/2 cups.)
Serve the stone crabs on a platter with the salsa and the mustard sauce.
The mustard sauce can be made several days in advance and stored in an airtight container.