We establish flexural deformation as a versatile route for engineering altermagnetism in two-dimensional collinear antiferromagnets. By tailoring the flexure, we selectively break different symmetries to realize altermagnetic states with distinct wave symmetries and reverse their spin splitting. A tight-binding model and first-principles calculations for monolayer MnPS3 demonstrate d- and i-wave states and a switchable transverse spin current in the d-wave state.