Due to their good dielectric properties and low global warming potential, C4F7N–CO2 and C4F7N–N2 mixtures have shown promising potential to replace SF6 in high voltage gas insulated equipment. However, during manufacturing, installation, and transportation of power equipment, burs and metal particles can be inevitably left inside, and they can cause corona discharge. Fundamental investigation of the corona discharge mechanism is essential to monitor partial discharge signals in environmentally friendly power equipment. This paper applies the fluid model to investigate the discharge mechanism of C4F7N–CO2 and C4F7N–N2 mixtures in negative point-plane corona discharge. A 2D axisymmetric model combines the drift-diffusion equations for electrons, positive ions, and negative ions and Poisson’s equation to study the process of dynamics. The gas is a mixture of C4F7N (5%, 7%, or 13%) and CO2 or N2 (95%, 93%, or 87%). The rise time of the first discharge pulse in C4F7N–CO2 and C4F7N–N2 mixtures is about 0.1 ns. The interval time between the first and the second pulse in the 5% C4F7N–95%CO2 mixture is about 1.5 times longer than that in the 5% C4F7N–95% N2 mixture. When the C4F7N content is 7% and 13%, the interval time between the first and second pulses in C4F7N–CO2 mixtures is about 2 and 3 times longer than those in C4F7N–N2 mixtures, respectively. The suppression regions in C4F7N–CO2 mixtures are larger than those in corresponding C4F7N–N2 mixtures. The total number of electrons, positive ions, and negative ions in C4F7N–CO2 mixtures is higher than that in C4F7N–N2 mixtures, while the reduced electric field in C4F7N–CO2 mixtures is smaller than that in C4F7N–N2 mixtures.