Two-dimensional multiferroic materials with controllable magnetism have promising prospects in miniaturized devices. By performing first-principle calculations, we predict that the MnF₄ monolayer is a ferroelastic semiconductor with an energy barrier of ∼160 meV f.u.⁻¹ and a reversible strain of 14.3%. Meanwhile, it is an antiferromagnetic material with an easy-axis along the b-axis and a Néel temperature of 190 K. The magnetic states and easy-axis can be switched by biaxial strain or carrier doping. Therefore, the MnF₄ monolayer is a promising material to study magnetic anisotropy and magneto-elastic coupling.