  We develop an iterative method for constructing four-dimensional generalized
unitarity cuts in $\mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory
coupled to fundamental matter hypermultiplets ($\mathcal{N} = 2$ SQCD). For
iterated two-particle cuts,specifically those involving only four-point
amplitudes, this implies simple diagrammatic rules for assembling the cuts to
any loop order, reminiscent of the rung rule in $\mathcal{N} = 4$ SYM. By
identifying physical poles, the construction simplifies the task of extracting
complete integrands. In combination with the duality between color and
kinematics we construct all four-point massless MHV-sector scattering
amplitudes up to two loops in $\mathcal{N} = 2$ SQCD, including those with
matter on external legs. Our results reveal chiral infrared-finite integrands
closely related to those found using loop-level BCFW recursion. The integrands
are valid in $D\leq 6$ dimensions with external states in a four-dimensional
subspace; the upper bound is dictated by our use of six-dimensional chiral
$\mathcal{N} = (1,0)$ SYM as a means of dimensionally regulating loop
integrals.
