Drain pineapple chunks, reserving the juice; set pineapple chunks aside.
In a 3-1/2- or 4-quart slow cooker combine carrots, onion, water chestnuts, sweet pepper, and celery. Top with pork. In a medium bowl whisk together reserved pineapple juice, the brown sugar, rice vinegar, tomato paste, tapioca, soy sauce, sherry (if desired), garlic, and sesame oil. Pour over all in cooker.
Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3-1/2 to 4 hours.
Stir in reserved pineapple chunks. Serve over hot cooked rice. If desired, sprinkle with green onions.