1. Process first 6 ingredients in a food processor or blender 15 seconds or until blended. Remove and reserve 3 Tbsp. rémoulade sauce mixture. Stir together remaining rémoulade sauce mixture, avocado, and tomato in a medium bowl.
2. Place half of crabmeat in 6 martini glasses. Top evenly with avocado mixture and remaining half of crabmeat. Drizzle each evenly with reserved 3 Tbsp. rémoulade sauce mixture (about 1 1/2 tsp. each). Spear 2 stuffed olives onto a wooden pick, and place in a glass; repeat with remaining stuffed olives. Serve immediately.