Preheat oven to 400°F. Coat a large rimmed baking sheet with cooking spray.
Toss sweet potatoes with oil and ⅛ tsp. each salt and pepper in the prepared pan. Bake, turning occasionally, until tender and brown, 20 to 25 minutes.
Meanwhile, combine ground beef, mushrooms, and the remaining ⅛ tsp. each salt and pepper in a medium bowl. Shape the mixture into 4 patties, about 4 inches in diameter.
Preheat grill to medium.
Oil the grill rack. Grill the burgers, covered, turning once, until an instant-read thermometer registers 160°F, 8 to 10 minutes total. Toast buns on the grill.
Combine mayonnaise and 1 tsp. Sriracha in a small bowl. Combine ketchup and the remaining 1 tsp. Sriracha in another small bowl. Spread the mayonnaise sauce on buns and top with the burgers, lettuce, tomatoes and onion. Serve with the sweet potatoes and the ketchup sauce for dipping.