The prolonged service life of civil engineering structures, such as buildings and highway pavement, means that they deteriorate with time, requiring frequent repair work. Polyurethane (PU) materials can effectively maintain engineering structures such as road pavement, runways, and buildings. Thus, the mechanical properties and dynamic performance of these materials for repair are essential to guarantee the safe usage of the facilities. This study investigated the strain–stress behavior and impact strength of polyurethane-based polymer concrete (PUPC) mixtures. Moreover, the tensile stress–strain behavior of rigid PU grout (PUGC) materials was evaluated. The result indicated that the U-shaped PUPC with 20% PU by weight experienced a maximum failure strain of 0.9% and 4.2% under static and dynamic loads, respectively. The average impact energy of PUPC was 3825% higher than that of normal concrete. According to PUGC’s mixing ratios, the average elastic modulus revealed an increasing trend, whereas ultimate strength, yield strain, yield stress, and failure stress showed a decreasing trend. Weibull distribution results showed that the probabilistic distribution of the impact strength followed the two-parameter Weibull distribution.