Kirigami, the art of introducing cuts in thin sheets to enable articulation and deployment, has become an inspiration for a novel class of mechanical metamaterials with unusual properties. Here we complement the use of periodic tiling patterns for kirigami designs by showing that quasicrystals can also serve as the basis for designing deployable kirigami structures, and analyze the geometrical, topological, and mechanical properties of these aperiodic kirigami structures.