To investigate the mechanical properties of cement concrete incorporating waste rubber powder, the response surface methodology was employed. The Box–Behnken central composite design was applied to analyze the three primary factors influencing the road performance of cement concrete containing waste rubber powder: the water–cement ratio, sand ratio, and waste rubber powder content. The study determined the impact of these factors on the flexural strength of waste rubber powder cement concrete at both 7 and 28 days. Additionally, the effects of the water–cement ratio, sand ratio, and waste rubber powder content on the performance of cement concrete were analyzed. To investigate the impact of waste rubber powder on cement concrete, various mechanical property tests were conducted, including compressive, flexural, dynamic elastic modulus, and impact performance tests. Furthermore, the study explored the influence of waste rubber powder on the noise reduction capacity of cement concrete using both the rubber ball impact method and ultrasonic method. Lastly, the durability of cement concrete with added rubber powder was assessed through shrinkage tests, frost resistance tests, and chloride ion penetration tests.