Coal and gas outburst is a complex dynamic disaster during coal underground mining. Revealing the disaster mechanism is of great significance for accurate prediction and prevention of coal and gas outburst. The geo-dynamic system of coal and gas outburst is proposed. The framework of geo-dynamic system is composed of gassy coal mass, geological dynamic environment and mining disturbance. Equations of stress–damage–seepage interaction for gassy coal mass is constructed to resolve the outburst elimination process by gas extraction with boreholes through layer in floor roadway. The results show the occurrence of outburst is divided into the evolution process of gestation, formation, development and termination of geo-dynamic system. The scale range of outburst occurrence is determined, which provides a spatial basis for the prevention and control of outburst. The formation criterion and instability criterion of coal and gas outburst are established. The formation criterion F₁ is defined as the scale of the geo-dynamic system, and the instability criterion F₂ is defined as the scale of the outburst geo-body. According to the geo-dynamic system, the elimination mechanism of coal and gas outburst—‘unloading + depressurization’ is established, and the gas extraction by boreholes through layer in floor roadway for outburst elimination is given. For the research case, when the gas extraction is 120 days, the gas pressure of the coal seam is reduced to below 0.4 MPa, and the outburst danger is eliminated effectively.