  Using a careful choice of infrared (IR) subtraction scheme, we demonstrate
the cancellation of all terms with transcendental weights 0,1,2 from the finite
part of the full-color two-loop four-gluon $\mathcal{N}=2$ supersymmetric QCD
amplitude, with $N_f$ massless supersymmetric quarks. This generalizes the
previously observed cancellation of weight-2 terms in the superconformal
theory, where $N_f=2N_c$ for gauge group SU$(N_c)$. The subtraction scheme
follows naturally both from general IR factorization principles and from an
integrand-level analysis of divergences in this amplitude. The divergences are
written in terms of scalar triangle integrals whose expressions are known to
all orders in the dimensional regulator $\epsilon=(4-D)/2$. We also present
integrated expressions for the full-color two-loop four-point amplitudes with
both matter and vectors on external legs in which lower-weight terms also
cancel using an appropriate IR scheme. This provides us with values for the
two-loop cusp, gluonic, and quark anomalous dimensions in $\mathcal{N}=2$
supersymmetric QCD, which are cross-checked between the three different
amplitudes.
