In this work, vacancy- and doped-induced magnetism engineering is investigated to functionalize the non-magnetic low-buckled hexagonal silicon sulfide (SiS) monolayer. This monolayer is an indirect gap semiconductor two-dimensional (2D) material with an energy gap of 2.20(3.02) eV obtained from the PBE(HSE06)-based calculations. Creating a single Si vacancy leads to a significant magnetization of SiS monolayer with the feature-rich half-metallic nature. Herein, a total magnetic moment of 1.89 μB is obtained and magnetic properties are produced mainly by S and Si atoms closest to the defect site. In contrast, single S vacancy preserves the non-magnetic nature inducing a band gap reduction of the order of 26.36%. n-type doping with P atom metalizes the monolayer, meanwhile As impurity leads to the emergence of the half-metallicity with a total magnetic moment of 1.00 μB. Similarly, this value is also obtained by p-doping using P and As atoms as dopants, where the diluted magnetic semiconductor nature is obtained. Moreover, doping with IA- (Na and K) and IIIA-group (Al and Ga) atoms is also proposed to engineer the magnetism in SiS monolayer. It is found that these impurities induce either half-metallic or diluted magnetic semiconductor behaviors with total magnetic moment between 0.99 and 1.00 μB. The electronic and magnetic properties are regulated mainly by the interactions between impurities and their neighbor S atoms, which modify the charge distribution in their outermost orbitals. In addition, the Bader charge analysis asserts that dopant atoms gain charge from the host monolayer when substituting S atom, meanwhile they act as charge loser — transferring charge to the host monolayer when doping at Si sublattice. The presented results may suggest efficient approaches to properly engineer SiS monolayer electronic and magnetic properties, making new 2D candidates for spintronic applications.