We present KiriPhys, a new type of data physicalization based on kirigami, a traditional Japanese art form that uses paper-cutting. Within the kirigami possibilities, we investigate how different aspects of cutting patterns offer opportunities for mapping data to both independent and dependent physical variables. As a first step towards understanding the data physicalization opportunities in KiriPhys, we conducted a qualitative study in which 12 participants interacted with four KiriPhys examples. Our observations of how people interact with, understand, and respond to KiriPhys suggest that KiriPhys: 1) provides new opportunities for interactive, layered data exploration, 2) introduces elastic expansion as a new sensation that can reveal data, and 3) offers data mapping possibilities while providing a pleasurable experience that stimulates curiosity and engagement.