Place wok over medium heat. Add the lime juice, mirin, fish sauce, lemongrass, scallions, and chile pepper; stir to combine.
Bring to a simmer; add the mussels. Cover, and let simmer, stirring occasionally, until the mussels have opened, 6 to 8 minutes. Remove from heat; remove and discard mussels that have not opened. Stir in the cucumber. Serve garnished with fresh cilantro and basil.