We study a single-wall carbon nanotube (SWNT) Polyvinyl alcohol (PVA) composite as a saturable absorber (SA) for pulse generation in Yb-doped fiber lasers. The saturable absorption and optical limiting (OL) characteristics of the SWNT device are investigated. By combing these two nonlinear effects, we find out for the first time, to the best of our knowledge, that mode-locking can be obtained in the dissipative soliton regime at low pumping followed by Q-switching at high pumping, which is quite different from conventional pulse dynamic evolutions. The Qswitched state operating at higher pump powers is due to the OL effect. The inverted operating fiber laser can be applied in various potential applications such as versatile material processing, optical communication and radar system etc.