Auxetics refer to a class of engineered structures which exhibit an overall negative Poisson’s ratio. These structures open up various potential opportunities in impact resistance, high energy absorption, and flexible robotics, among others. Interestingly, auxetic structures could also be tailored to provide passive adaptation to changes in environmental stimuli — an adaptation of this concept is explored in this paper in the context of designing a novel load-adaptive gripper system. Defining the design in terms of repeating parametric unit cells from which the finite structure can be synthesized presents an attractive computationally-efficient approach to designing auxetic structures. This approach also decouples the optimization cost and the size of the overall structure, and avoids the pitfalls of system-scale design e.g., via topology optimization. In this paper, a surrogate-based design optimization framework is presented to implement the concept of passively load-adaptive structures (of given outer shape) synthesized from auxetic unit cells. Open-source meshing, FEA and Bayesian Optimization tools are integrated to develop this computational framework, enhancing it adopt-ability and extensibility. Demonstration of the concept and the underlying framework is performed by designing a simplified robotic gripper, with the objective to maximize the ratio of towards-load (gripping) horizontal displacement to the load-affected vertical displacement. Optimal auxetic cell-based design generated thereof is found to be four times better in terms of exhibited contact reaction force when compared to a design obtained with topology optimization that is subjected to the same specified maximum loading.