Controlling the electronic and magnetic properties of two-dimensional (2D) materials is a key step to make new multifunctional candidates for practical applications. In this work, defects and doping with transition metals (TMs = V, Cr, Mn, and Fe) at Ge sublattices are proposed in order to develop novel features in the hexagonal germanium arsenide (GeAs) monolayer. The pristine GeAs monolayer is a non-magnetic indirect gap semiconductor with an energy gap of 1.20(1.82) eV as provided by PBE(HSE06)-based calculations. A single Ge vacancy metallizes the monolayer, preserving its non-magnetic nature. In contrast, significant magnetization with a total magnetic moment of 1.96 μ B is achieved by a pair of Ge vacancies. Herein, the computed band structures assert the half-metallic behavior of the defective system. Similarly, half-metallicity is also obtained by V, Mn, and Fe doping. Meanwhile, the Cr-doped GeAs monolayer is classified as a diluted magnetic semiconductor 2D system. In these cases, magnetic properties are produced mainly by TM-3d electrons with total magnetic moments between 2.00 and 4.00 μ B. Further, the effects of substituting a pair of Ge atoms with a pair of TM atoms (pTMGe systems) are also investigated. Results indicate the ferromagnetic half-metallicity of the pVGe system, meanwhile antiferromagnetic ordering is stable in the remaining cases. In all cases, TM impurities transfer charge to the host GeAs monolayer since they are surrounded by As atoms, which are more electronegative than dopant atoms. Results presented herein may introduce new 2D systems - made from the non-magnetic GeAs monolayer - for spintronic applications with suitable electronic and magnetic features controlled mainly by transition metals.