In a recent advance, zirconium triselenide (ZrSe3) nanosheets with anisotropic and strain-tunable excitonic response were experimentally fabricated. Motivated by the aforementioned progress, we conduct first-principle calculations to explore the structural, dynamic, Raman response, electronic, single-layer exfoliation energies, and mechanical features of the ZrX3 (X = S, Se, Te) monolayers. Acquired phonon dispersion relations reveal the dynamical stability of the ZrX3 (X = S, Se, Te) monolayers. In order to isolate single-layer crystals from bulk counterparts, exfoliation energies of 0.32, 0.37, and 0.4 J/m2 are predicted for the isolation of ZrS3, ZrSe3, and ZrTe3 monolayers, which are comparable to those of graphene. ZrS3 and ZrSe3 monolayers are found to be indirect gap semiconductors, with HSE06 band gaps of 1.93 and 1.01 eV, whereas the ZrTe3 monolayer yields a metallic character. It is shown that the ZrX3 nanosheets are relatively strong, but with highly anisotropic mechanical responses. This work provides a useful vision concerning the critical physical properties of ZrX3 (X = S, Se, Te) nanosheets.