A new and unique X Mangave plant named ‘Catch a Wave’ characterized by a compact mound of bluish-green, thick, lanceolate, coarsely sinuate, folded to concaved foliage. Marginal and apical spines are soft and flexible. Leaves develop small, irregular, greyed-purple spots with strong ultra violet light. The new plants is suitable for the garden landscape or as a potted plant in the garden or around the home.