Gaseous emissions from animal manure are considerable contributor to global ammonia (NH3) and agriculture greenhouse gas (GHG) emissions. Given the demand to promote mitigation of GHGs while fostering sustainable development of the Paris Agreement, an improvement of management systems is urgently needed to help mitigate climate change and to improve atmospheric air quality. This study presents a meta-analysis and an integrated assessment of gaseous emissions and mitigation potentials for NH3, methane (CH4), and nitrous oxide (N2O) (direct and indirect) losses from four typical swine manure management systems (MMSs). The resultant emission factors and mitigation efficiencies allow GHG and NH3 emissions to be estimated, as well as mitigation potentials for different stages of swine operation. In particular, changing swine manure management from liquid systems to solid–liquid separation systems, coupled with mitigation measures, could simultaneously reduce GHG emissions by 65% and NH3 emissions by 78%. The resultant potential reduction in GHG emissions from China’s pig production alone is greater than the entire GHG emissions from agricultural sector of France, Australia, or Germany, while the reduction in NH3 emissions is equivalent to 40% of the total NH3 emissions from the European Union. Thus, improved swine manure management could have a significant impact on global environment issues.