In open quantum systems, non-trivial transport properties are commonly achieved using inhomogeneous setups, for example, by coupling systems to different baths at their edges. Interestingly, this is not the only viable approach. We demonstrate that nonreciprocal dissipative processes applied to the bulk can also generate and control both charge and spin currents in a two-dimensional spinful fermionic atom quantum system with broken inversion and time-reversal symmetries. Within the Gorini-Kossakowski-Sudarshan-Lindblad master equation formalism and using an approach based on the time-dependent generalized Gibbs ensemble, we identify in the weak dissipative coupling regime the minimal set of nonreciprocal jump operators required to induce charge and spin currents and to control both their direction and magnitude.