Pat the squid dry. If using whole squid, lightly score the body in a crisscross pattern. Mix the dark soy sauce, light soy sauce, and turmeric powder, then coat the squid and marinate for 30 minutes.
While the squid marinates, light a charcoal grill (or preheat a grill pan). Lightly oil the grill grates.
Make the nam jim seafood by pounding the garlic and green chilies in a mortar and pestle. Add the coriander and mint, then stir in the fish sauce, lime juice, and sugar until combined.
Once the grill is hot, grill the squid over high heat for 2–3 minutes per side, until opaque with lightly charred edges. Avoid overcooking.
Slice into bite-sized pieces if desired and serve immediately with the nam jim seafood for dipping.