Bring water and 1/2 teaspoon salt to a boil in a saucepan. Add barley; cover and simmer until tender yet firm to the bite, about 20 minutes. Drain any excess cooking liquid and let cool completely, 20 to 30 minutes.

Mash 1/4 of the mango against the side of a large bowl using a fork or potato masher. Whisk in lime juice, olive oil, cumin, and 1/2 teaspoon salt. Add barley, remaining mango, black beans, grape tomatoes, red onion, cilantro, and jalapeno; toss until well-combined.