DC arc behavior is normally a complicated and rapid time-dependent evolution process. To investigate the climbing behavior, dynamic properties, as well as the self-extinction mechanism, an experimental platform in collaboration with a pair of Jacob’s ladder electrodes was established. The overall evolution process including arc generation, arc combustion, and arc self-extinction was well accomplished. The dynamic climbing behavior and dynamic emission spectrum were captured. The dynamic volt-ampere characteristic, excitation temperature and electron density were all analyzed during the overall evolution process. Furthermore, the self-extinction mechanism under the function of Jacob’s ladder electrodes was explored. The experimental observations show that a two-stage climbing behavior is performed in succession. The dynamic resistance is fluctuated significantly in purple arc stage, while it is stable in yellow arc stage. The excitation temperature is positively correlated with arc current, but not strictly linear. The co-action results of two dynamic features make it more favorable for quick separation from the external ability of power supply. As a result, the arc is transitioned from self-sustaining state to non-self-sustaining state. This paper is regarded as a preliminary research aiming to provide some references for dynamic properties and self-extinction mechanism of the climbing arc in arcing horn.