Experiments are conducted on a rotating detonation engine fed by Hydrogen and Air. Spinning pulsed detonation mode is identified for the first time. Characterized by evident spiral and pulsed features, this mode exhibits two distinctive types: single-wave pattern where one circumferentially propagating transverse wave is attached to a longitudinal pulsed detonation and two-wave pattern where two circumnavigating transverse waves are attached to a longitudinal pulsed detonation. The inception, sustenance, and transition of this novel mode are described and analyzed. Moreover, a propagation mechanism for spinning pulsed detonation mode is proposed by analogy with that of different detonation phenomena, i.e., spinning detonation wave in a round tube and rotating detonation wave in an RDE. A trade-off relationship between the longitudinal pulsed detonation and the attached transverse wave is reflected in spinning pulsed detonation mode, explaining the prevalent mode switch between longitudinal pulsed detonation mode and rotating detonation mode in RDEs. The validity of this proposed propagation mechanism is verified by the data of pressure signals and high-speed photography.