Black Arsenic-phosphorus (AsP) monolayer is a novel two-dimensional nanomaterial with the characteristics of modest direct bandgap and superhigh carrier mobility. However, little is known about how the surface adsorption affects the property of AsP monolayer. Motivated by this, we researched systematically the geometry, adsorption energy, magnetic moment and electronic structure of 11 different adatoms adsorbed on AsP monolayer using first-principles calculations. The adatoms used in this study include light nonmetallic (C, N, O) adatoms, period-3 metal (Na, Mg, Al) adatoms, and transition-metal (Ti, V, Cr, Mn, and Fe) adatoms. The adatoms cause an abundant variety of structural, magnetic and electronic properties. This study shows that AsP binds strongly with all adatoms under study and the adsorption energies in all systems are much stronger than that on graphene, SiC, BN, or MoS2. The semiconductor property of AsP is affected by the introduction of adsorbed atoms, which can induce mid-gap states or cause n-type doping. Moreover, the adatom adsorptions cause various spintronic characteristics: N-, Ti-, and Fe-adsorbed AsP become bipolar semiconductors, while the Mn-decorated AsP becomes a bipolar spin-gapless semiconductor. Our results suggest that atomic adsorption on AsP monolayers has potential application in the field of nanoelectronics and spintronics.