Significance Collagen plays crucial biomechanical roles in a wide array of animal tissues, but its mechanical properties remain largely static over short timescales. However, echinoderms (sea cucumbers, starfish) are striking exceptions to this rule, having “mutable collagenous tissue” with changeable mechanical properties, enabling complex locomotion, postural maintenance, defense, and reproductive strategies. Using a high-resolution X-ray probe that measures how the building blocks—fibrils—of echinoderm connective tissue stretch, slide, or reorient in real time, we show that sea cucumbers achieve this remarkable property by changing the stiffness of the matrix between individual fibrils, rather than the properties of the fibrils themselves. Understanding the mechanisms of mutability in this unique tissue may help design novel mechanically tunable synthetic biomaterials.