The blow-off is one of the typical flame extinction mechanisms, and such a principle has been widely used in firefighting when the water-based extinguisher is limited. This work explores the blow-off extinctions of different diffusion flames by air vortex ring. The vortex ring harnesses its kinetic energy within the fast-rotating vortex core, enabling the transmission of power over several meters to blow off a remote flame. The power required for vortex ring blow-off is found to be two to three orders of magnitude smaller than the power of the flame itself, demonstrating exceptional energy efficiency. It is observed that the poloidal flow (circulation) surrounding the vortex core can stretch the flame base to the critical state and then cause instantaneous extinction. To explain the vortex-induced blow-off limit, a critical Damköhler number that accounts for the competition between fuel gas flow and flame stretch was formulated. This work provides a fundamental understanding of the extinction mechanism by vortex ring, and it offers technical guidelines for using air as a flame extinguisher for remote firefighting within minimum energy input.