Chop the celery, red onion, green onions, and cilantro finely for mixing. Thinly slice cucumber, red bell pepper, and carrots into matchsticks for the wrap.
In a small bowl, mash the tuna and avocado together until creamy and combined.
Stir in sriracha, Dijon mustard, chopped celery, red onion, green onions, cilantro, salt, and pepper. Mix well.
Lay out each tortilla and place leafy greens in the center, followed by sliced veggies.
Divide the spicy tuna mixture evenly among the tortillas.
Tightly roll up the wraps and slice in half if desired. Serve immediately.