We analytically investigate the Fano-type optical response and the four-wave mixing (FWM) process by exploiting the magnetoelasticity of a ferromagnetic material. The deformation of the ferromagnetic material plays the role of mechanical displacement, which is simultaneously coupled to both optical and magnon modes. We report that the magnetostrictively induced displacement leads to realization of Fano profiles in the output field and is effectively well-tuned through adjusting the system parameters, such as effective magnomechanical coupling, magnon detuning, and cavity detuning. It is found that the magnetoelastic interaction also gives rise to the FWM phenomenon. The number of the FWM signals mainly depends upon the effective magnomechanical coupling and the magnon detuning. Moreover, the FWM spectrum exhibits suppressive behavior upon increasing (decreasing) the magnon (cavity) decay rate. The present scheme will open new perspectives in highly sensitive detection and quantum information processing.