In this paper, the high-repetition-rate passively Q-switched (PQS) and the femtosecond continuous-wave mode-locked (CWML) lasers are successfully obtained with 2D black arsenic-phosphorus (b-AsP) nanosheets as saturable absorber (SA) at 1 μm for the first time, to the best of our knowledge. The saturable absorption properties and ultrafast carrier dynamics of the 2D b-AsP SA are explored by Z-scan and pump-probe techniques. Moreover, according to the measurement of desired nonlinear optical characteristics of the relaxation time of 27 ps and the modulation depth of 7.14%, the PQS and CWML lasers are demonstrated with the highest repetition rate of 2.26 MHz in the PQS laser and the pulse width of 470 fs in the CWML laser. The results show 2D b-AsP SA has enormous potential for pulse modulation in solid-state bulk lasers.