Piezoresistive sensors are widely used because of their simple fabrication process and low cost, and their performance is usually improved via a single method, such as creating microstructures or adjusting material mechanical properties. In this study, when the two methods are combined, a high-sensitivity flexible sponge sensor capable of sensing tiny pressures with surface hemispheres was designed, and mathematical models for its sensing response caused by compression deformation were established. Hydroxylated carbon nanotubes (CNT-OH) modified with carbon nanotubes (CNTs) were filled in a polydimethylsiloxane (PDMS) matrix, along with a poreformer, and poured into a mold to obtain a CNT-OH/PDMS sponge piezoresistive layer with a hemispherical array on its surface. The deformation equation of the piezoresistive layer under external pressure, the function of the contact area between the surface hemispherical array and the electrode, and the sensitivity model of the sensor were subsequently established. The effects of the material porosity and diameter of the surface hemispherical array on the performance of the sensor were investigated. An increase in the material porosity and a decrease in the hemispherical diameter of the piezoresistive layer are helpful for improving the sensitivity of the sensor and its ability to detect tinier pressure. The measurement range and response time of the sensor are determined mainly by the mechanical properties of the piezoresistive layer material. These experimental results were consistent with our theoretical conclusions. This sensor can accurately detect the number of seeds sown by agricultural seeders each time and can identify the frequency of human vocal cord vibrations, pulse beats, and wrist movements.