Conventional asphalt roads are noisy. Currently, there are two main types of mainstream noise-reducing pavements: pore acoustic absorption and damping noise reduction. However, a single noise reduction method has limited noise reduction capability, and porous noise-reducing pavements have a shorter service life. Therefore, this paper aimed to improve the noise-damping performance of porous asphalt mixture by adding rubber granules and extending its service life using electromagnetic induction heating self-healing technology. Porosity and permeability coefficient test, Cantabro test, immersion Marshall stability test, freeze-thaw splitting test, a low-temperature three-point bending experiment, and Hamburg wheel-tracking test were conducted to investigate the pavement performance and water permeability coefficients of the mixtures. A tire drop test and the standing-wave tube method were conducted to explore their noise reduction performance. Induction heating installation was carried out to study the heating rate and healing performance. The results indicated that the road performance of the porous asphalt mixture tends to reduce with an increasing dosage of rubber granules. The road performance is not up to the required standard when the dosage of rubber granules reaches 3%. The mixture's performance of damping and noise tends to increase with the increase of rubber granule dosage. Asphalt mixtures with different rubber granule dosages have different noise absorption properties, and the mixture with 2% rubber granules has the best overall performance (a vibration attenuation coefficient of 7.752 and an average absorption factor of 0.457). The optimum healing temperature of the porous asphalt mixture containing rubber granules and steel wool fibers is 120 °C and the healing rate is 74.8% at a 2% rubber granule dosage. This paper provides valuable insights for improving the noise reduction performance and service life of porous asphalt pavements while meeting road performance standards.