Heavy metal pollution has a negative impact on both human health and the environment. The monitoring of heavy metal is therefore very important from a practical standpoint. In this study, the adsorption energy, charge transfer, band, densities of states, and sensitivity of SnSe monolayers toward heavy metals (As, Cd, Cr, Hg, Ni, Pb) were investigated using density functional theory combined with the non-equilibrium Green's function approach. The calculations show that SnSe monolayers have excellent sensitivities exceeding the limit of quantitation (LOQ) towards As, Cd, Hg, and Pb, which are as high as 384467%, 1462%, 1791%, and 26160%, respectively. Moreover, analyzing response peaks at various bias voltages can identify the composition of heavy metals from diverse sources, providing valuable insights for selective heavy metal monitoring. SnSe monolayers exhibit wide bias voltage windows that enhance sensor sensitivity by reaching the detection threshold, while also simplifying sensor encapsulation, resulting in higher reliability. The SnSe monolayer exhibits rapid recovery times for As, Hg, and Cd at room temperature, while for Pb, heating to 498 K is required for rapid recovery. These findings show that SnSe monolayers have a strong potential for constructing extremely sensitive and selective heavy metal sensors that are also reusable, implying that SnSe monolayers might serve as a possible online sensor for environmental monitoring.