Prepare the blackberry sauce. Add the rice vinegar, fresh blackberries, honey, ginger, lemongrass, sesame oil, and a small amount of salt and black pepper to a food processor or blender.
Blend until smooth. Process until the berries are completely pureed and the ingredients form a smooth blackberry sauce. Taste and adjust the seasoning as needed. Set aside.
Prepare the salmon. Pat the salmon fillets dry with paper towels. Brush the surface of each fillet evenly with chili garlic sauce.
Preheat the grill. Heat an outdoor grill or grill pan to medium heat. Clean and thoroughly oil the grates to reduce sticking.
Grill the salmon. Place the salmon on the grill and cook for approximately 4–5 minutes on the first side. Carefully turn and cook for another 3–5 minutes, depending on thickness and your preferred doneness.
Check for doneness. The Grilled Salmon with Blackberry Sauce should be opaque and flake easily with a fork. For food safety, the USDA recommends cooking fish to an internal temperature of 145°F (63°C).
Rest. Transfer the grilled salmon to a plate and allow it to rest for about 5 minutes.
Serve. Spoon the fresh blackberry sauce over or alongside the salmon. Serve immediately with your favorite green vegetables or another light side dish.