Pat the salmon dry with paper towels.
Season both sides with salt and pepper.
Add mango, soy sauce, water, honey, rice vinegar, ginger, garlic, and sesame oil to a small pan.
Simmer the sauce over medium heat for 5 to 7 minutes.
Mash some mango pieces with a spoon while the sauce cooks.
Stir cornstarch with cold water in a small bowl.
Add the slurry to the sauce and stir until glossy.
Heat oil in a large skillet over medium heat.
Cook skin-on salmon skin-side down for 4 to 5 minutes.
Flip and cook 2 to 4 minutes more, based on thickness.
Spoon the mango teriyaki glaze over the salmon.
Add green onions, sesame seeds, and fresh lime juice.