Abstract Solvent‐responsive shape memory polymers (SR‐SMPs) are smart materials that can retain their original shape when exposed to solvents. However, most reported SR‐SMPs show slow shape recovery and lack multi‐solvent responsiveness, which greatly limits their practical use. Here, a novel SR‐SMP is introduced by creating a dual‐component network comprising aliphatic polyurethane acrylate (AUA) and polystyrene‐block‐polyisoprene‐block‐polystyrene (SIS). The AUA phase provides mechanical stability and prevents excessive swelling, while the SIS phase, compatible with low‐polarity solvents, promotes plasticization and speeds up shape recovery. This results in excellent shape memory performance when exposed to various solvents. The incorporation of carbon nanotubes (CNTs) and carbon black (CB) further accelerates shape recovery to about 20 s, which is over an order of magnitude faster than previously reported SR‐SMPs. Based on these properties, a dual‐mode sensor is developed using the SR‐SMP, capable of providing both visual and electrical responses when exposed to petroleum ether vapor. The visual shape change offers an intuitive indication, while the electrical signal delivers a more accurate output, with a detection limit of 0.013 g·L −1 and a sensitivity of 1519.8 L·g −1 . The as‐developed SR‐SMP exhibits great promise in the creation of next‐generation solvent‐driven smart materials.