Skeletal tissues are built and shaped through complex, interacting active and passive processes. These spatial and temporal variabilities make interpreting growth mechanisms from morphology difficult, particularly in bone, where the remodeling process erases and rewrites local structural records of growth throughout life. In contrast to the majority of bony vertebrates, the elasmobranch fishes (sharks, rays, and their relatives) have skeletons made of cartilage, reinforced by an outer layer of mineralized tiles (tesserae), which are believed to grow only by deposition, without remodeling. We exploit this structural permanence, performing the first fine-scale correlation of structure and material properties in an elasmobranch skeleton. Our characterization across an age series of stingray tesserae allows unique insight into the growth processes and mechanical influences shaping the skeleton. Correlated quantitative backscattered electron imaging (qBEI) and nanoindentation measurements show a positive relationship between mineral density and tissue stiffness/hardness. Although tessellated cartilage as a whole (tesserae plus unmineralized cartilage) is considerably less dense than bone, we demonstrate that tesserae have exceptional local material properties, exceeding those of (mammal) bone and calcified cartilage. We show that the finescale ultrastructures recently described in tesserae have characteristic material properties suggesting distinct mechanical roles and that regions of high mineral density/stiffness in tesserae are confined predominantly to regions expected to bear high loads. In particular, tesseral spokes (laminated structures flanking joints) exhibit particularly high mineral densities and tissue material properties, more akin to teeth than bone or calcified cartilage. We conclude that these spokes toughen tesserae and reinforce points of contact between them. These toughening and reinforcing functions are supported by finite element simulations incorporating our material data. The high stresses predicted for spokes, and evidence we provide that new spoke laminae are deposited according to their local mechanical environment, suggest tessellated cartilage is both mutable and responsive, despite lacking remodeling capability. Statement of Significance: The study of vertebrate skeletal materials is heavily biased toward mammal bone, despite evidence that bone and cartilage are extremely diverse. We broaden the perspective on vertebrate skeleton materials and evolution in an investigation of stingray tessellated cartilage, a curious type of unmineralized cartilage with a shell of mineralized tiles (tesserae). Combining high-resolution imaging and material testing, we demonstrate that tesserae have impressive local material properties for a vertebrate skeletal tissue, arguing for unique tissue organization relative to mammalian calcified cartilage and bone. Incorporating our materials data into mechanical models, we show that finescale material arrangements allow this cartilage to act as a functional and responsive alternative to bone, despite lacking bone's ability to remodel. These results are relevant to a diversity of researchers, from skeletal, developmental, and evolutionary biologists, to materials scientists interested in high-performance, low-density composites.