The performance of flexible and stretchable sensors relies on the optimization of both the flexible substrate and the sensing element, and their synergistic interactions. Herein, a novel strategy is reported for cost-effective and scalable manufacturing of a new class of porous materials as 3D flexible and stretchable piezoresistive sensors, by assembling carbon nanotubes onto porous substrates of tunable Poisson ratios. It is shown that the piezoresistive sensitivity of the sensors increases as the substrate's Poisson's ratio decreases. Substrates with negative Poisson ratios (auxetic foams) exhibit significantly higher piezoresistive sensitivity, resulting from the coherent mode of deformation of the auxetic foam and enhanced changes of tunneling resistance of the carbon nanotube networks. Compared with conventional foam sensors, the auxetic foam sensor (AFS) with a Poisson's ratio of -0.5 demonstrates a 300% improvement in piezoresistive sensitivity and the gauge factor increases as much as 500%. The AFS has high sensing capability, is extremely robust, and capable of multimodal sensing, such as large deformation sensing, pressure sensing, shear/torsion sensing, and underwater sensing. AFS shows great potential for a broad range of wearable and portable devices applications, which are described by reporting on a series of demonstrations.