We propose a two-dimensional (2D) tetragonal material: an yttrium nitride (t-YN) monolayer, with a distinguished combination of mechanical and electronic properties based on first-principles calculations. We find that the t-YN monolayer is a low direct band gap semiconductor (0.55 eV) with strong anisotropic mechanical and electronic properties. We also identify that the t-YN monolayer to be a 2D ferroelastic material with a reversible strain of about 14.4%, indicating that the anisotropic properties of the t-YN monolayer can be switched by applying external stress. Furthermore, the moderate-switching barrier (33 meV/atom) of ferroelastic lattice rotation renders the switchable anisotropic properties accessible experimentally. These outstanding properties make the t-YN monolayer a promising switchable anisotropic 2D material for electronic and mechanical applications.