In this work we present SCRAMBLE, a configurable neuromorphic architecture that provides security against different threats by employing memristors for critical parts and functions. More specifically, we employ memristive memory cells - that are 3D stacked on top of the configurable neuromorphic hardware - to securely hold the weights as well as activation functions of any model processed on the generalized architecture. Thus, programmable memristive cells enable reconfiguration of the architecture to thwart both model stealing and hardware IP stealing attacks. We implement a proof-of-concept for the proposed architecture and analyze its security metrics. We also benchmark it against selected prior art for neuromorphic architectures to quantify the security-performance trade-offs.