The extinction of a premixed flame propagating in a stagnation-point flow under the influence of an inert spray is studied using activation energy asymptotics. A completely prevaporized and partially prevaporized spray are identified on the basis of a critical value of the initial droplet size for completing the vaporization process at the flame. Parameters for flame extinction consist of the liquid loading and the droplet size of the spray indicating the internal heat loss associated with liquid vaporization, and the flow stretch which strengthens and weakens the burning strength of the Le < 1 and Le > 1 flame, respectively. The Le < 1 flame can be extinguished when it endures a small flow stretch and experiences a partially prevaporized inert spray with the liquid loading and the droplet size large enough. Furthermore, flame extinction of the Le < 1 flame by the inert spray is characterized by a S-shaped curve. Conversely, results for the Le > 1 flame show that flame extinction is possible for the flame with and without the inert spray; and that there is an abrupt change on extinction characteristics in response to varying the droplet size. Finally, the flow stretch and the inert spray are responsible for extinction of the Le < 1 flame identified by a C-shaped curve and a W-shaped curve, respectively.