Thiophene and two derivatives (2-methylthiophene and 3-methylthiophene) have been detected on the surface of Mars with the Sample Analysis at Mars instrument suite onboard NASA's Curiosity rover. Thiophene could serve as a secondary chemical biosignature since the secondary biosynthesis of thiophene is considered an important production pathway. However, it is critical to understand the abiotic formation and destruction of thiophene and its derivatives since these pathways could affect the molecules' stabilities on planetary surfaces over geological timescales. Here, we present the radiolytic destruction kinetics of thiophene, 2-methylthiophene, and 3-methylthiophene as single-component ices and when diluted in water ice at low temperatures. Using infrared spectroscopy, we determined the destruction rate constants and extrapolated our radiolytic half-lives to the surface of Mars, assuming the measured and modeled surface dose rates. We found that our rate constants strongly depend on temperature and presence of water ice. Based on our determined radiolytic half-life for thiophene under conditions most similar to those of thiophene groups in Martian macromolecules, we expect thiophene to be stable on the surface for significantly longer than the Martian surface exposure age of sites in Gale crater where thiophenes have been detected.