The viscoelastic behavior of asphalt mixtures is a crucial consideration in the analysis of pavement mechanical responses and structural design. This study aims to elucidate the molecular structure and component evolution trends of polyphosphoric acid (PPA)/styrene butadiene styrene block copolymer (SBS)/styrene butadiene rubber copolymer (SBR) composite modified asphalt (CMA) under rolling thin film oven test (RTFOT) and pressure aging (PAV) conditions, as well as to analyze the viscoelastic evolution of CMA mixtures. First, accelerated aging was conducted in the laboratory through RTFOT, along with PAV tests for 20 h and 40 h. Next, the microscopic characteristics of the binder at different aging stages were explored using Fourier-transform infrared spectroscopy (FTIR) and gel permeation chromatography (GPC) tests. Additionally, fundamental rheological properties and temperature sweep tests were performed to reveal the viscoelastic evolution characteristics of CMA. Ultimately, the viscoelastic properties of CMA mixtures under dynamic loading at different aging stages were clarified. The results indicate that the incorporation of SBS and SBR increased the levels of carbonyl and sulfoxide factors while decreasing the level of long-chain factors, which slowed down the rate of change of large molecule content and reduced the rate of change of LMS by more than 6%, with the rate of change of overall molecular weight distribution narrowing to below 50%. The simultaneous incorporation of SBS and SBR into CMA mixtures enhanced the dynamic modulus in the 25 Hz and -10 °C range by 24.3% (AC-13), 15.4% (AC-16), and reduced the φ by 55.8% (AC-13), 40% (AC-16). This research provides a reference for the application of CMA mixtures in the repair of pavement pothole damage.