To achieve high-value utilization of biogas and nitrogen-rich biogas slurry, this study employed vacuum membrane distillation (VMD) to separate and concentrate ammonia nitrogen from biogas slurry into green ammonia solution, which was subsequently used for biogas CO2 capture. The recovery performance of ammonia nitrogen from biogas slurry and the CO2 absorption characteristics of the produced aqueous ammonia solution were systematically investigated. Results showed that increasing the biogas slurry pH and initial ammonia nitrogen concentration significantly enhanced the aqueous ammonia concentration in the recovered green aqueous ammonia solution. Notably, when the initial biogas slurry concentration was 6 g-N/L and the pH was adjusted to 10, the aqueous ammonia concentration in the green aqueous ammonia solution reached 28.03 g-N/L. Moreover, coupling the permeate-side pressure with the biogas slurry temperature—while ensuring that the permeate pressure matched the corresponding saturated vapor pressure of water—yielded markedly higher ammonia separation factors and aqueous ammonia concentrations than adjusting either parameter alone. At an initial concentration of 1.5 g-N/L, under 60 °C and 20 kPa, the ammonia separation factor reached 15.86 after 6 h of operation, and the aqueous ammonia concentration reached 6.58 g-N/L. The CO2 absorption performance of the green aqueous ammonia solution was strongly influenced by the aqueous ammonia concentration, liquid velocity rate, and biogas flow velocity. When the aqueous ammonia concentration was 0.7 mol/L, with a liquid flow velocity of 60 mL/min and a biogas flow velocity of 0.3 L/min, the CO2 removal efficiency reached 98.79%. Although high concentrations of volatile fatty acids exhibited some inhibitory effect on CO2 absorption, the impurity levels in practical aqueous ammonia solution are typically low; thus, the recovered green aqueous ammonia solution can provide excellent CO2 capture performance.