Stir together 2 cups raspberries, onions, ketchup, vinegar, brown sugar, brown mustard, and Worcestershire sauce in a 6-quart slow cooker.

Trim excess fat from pork, if desired. Combine salt, garlic powder, smoked paprika, and pepper in small bowl. Sprinkle and rub over pork roast. Place pork in slow cooker; turn to coat with sauce. Cover and cook on HIGH 5 to 6 hours or LOW 8 to 10 hours or until meat is fork tender (210°).

Transfer pork to cutting board. Transfer half of cooking juices with raspberries and onions to food processor or blender. Cover and process until smooth. Return sauce mixture to slow cooker. Repeat processing remaining cooking juices; return to slow cooker. Shred pork using 2 forks. Return pork to slow cooker; stir to coat with sauce. Cover; keep warm.

Combine salad kit greens, toppings, and dressing in medium bowl. Cut remaining 1 cup raspberries in half; add to salad mixture and toss to combine.

To serve, spoon pork mixture on bun bottoms. Top with salad mixture and bun tops.