In a large bowl, whisk together mustard, lime juice, and oil; season with salt and pepper. Add onion, bell pepper, and mango; toss to combine. Set aside.
Lay tortillas on a work surface; dividing evenly, line each with spinach, leaving a 1-inch border all around. Arrange beef slices down center of each wrap. Top beef with mango mixture and any juices from bowl.
Fold in two opposite sides, and roll up wraps tightly; cut in half.
For Black Bean Relish: In a medium bowl, combine 1/2 medium red onion, finely chopped, one can (15.5 ounces) black beans, rinsed and drained 1 cup chopped fresh cilantro, 2 tablespoons fresh lime juice, and 1 tablespoon olive oil. Season with salt and pepper.