Multiple strain-induced effects beyond the piezoelectric effect in altermagnetic monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Co</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>MoSe</mml

The two-dimensional (2D) altermagnet (AM) is regarded as a promising candidate to achieving spintronic and valleytronic devices due to its large nonrelativistic spin splitting and high-density integration. It is crucial to explore the manipulation mechanism of spin, valley polarization, and piezoelectric response in the 2D AM system. We perform first-principles calculations to study monolayer ${\mathrm{Co}}_{2}{\mathrm{MoSe}}_{4}$ and find that it is an AM semiconductor with a N\'eel temperature of $\ensuremath{\sim}$84 K. The ${\mathrm{Co}}_{2}{\mathrm{MoSe}}_{4}$ monolayer has a 0.97 eV direct band gap located at the X/Y valley, and the valley degeneracy is protected by the crystal symmetry. Furthermore, this monolayer exhibits large spin splittings of 0.53 and 0.45 eV for the valence and conduction bands, respectively. Our calculations reveal that uniaxial strain could give rise to significant valley polarization and asymmetric distributions of Berry curvature due to the diagonal mirror symmetry breaking. It is predicted that the strain-driven magnetic response switching characterized with nonzero net magnetization can be realized by using hole doping combined with an in-plane strain. This monolayer is expected to be an excellent shear-type piezoelectric candidate with an impressive piezoelectric coefficient. The monolayer could exhibit the multipiezo effect induced by uniaxial strain, including the piezoelectricity, piezovalley, piezomagnetism, and anomalous valley Hall effect. Our findings provide not only a perspective for exploring the versatility of the 2D AM but also a platform to develop next-generation multifunctional devices.