The cut sequence describes the failure mode of the dynamic system, whose dynamic behaviors make the generation of cut sequence set very complicated. This paper brings forward the conception of extended cut sequence, which is incorporated with temporal logic and has more expressive capability than previous similar conceptions. According the type of logic gate, the minimal extended cut sequence set is generated using the basic set manipulation (union, intersection, difference and product). The expression form and generation process based on extended cut sequence are more efficient than that based on traditional cut sequence. As an example, apply this method to a famous hypothetical dynamic system. The system is modeled by dynamic fault tree and the minimal extended cut sequences are generated and analyzed. The result shows that this method can quickly acquire precise minimal extended cut sequence set.