Perturbative renormalization of chiral nuclear forces at subleading order in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:m

We investigate renormalization of chiral nuclear forces in the coupled channel of ${}^{3}{S}_{1}\ensuremath{-}{}^{3}{D}_{1}$ of nucleon-nucleon scattering. The one-pion exchange potential is treated nonperturbatively at leading order while subleading potentials are perturbations. Very much like the uncoupled channel of ${}^{3}{P}_{0}$, the singular attraction of one-pion exchange gives rise to the so-called genuine exceptional cutoffs, where artificial correlations between subleading contact operators emerge and they result in ill-defined values of the low-energy constants. To address this issue we follow the solution proposed for ${}^{3}{P}_{0}$ in [Peng et al., Phys. Rev. C 110, 054001 (2024)] and apply it to ${}^{3}{S}_{1}\ensuremath{-}{}^{3}{D}_{1}$. The truncation uncertainty of an effective field theory allows certain degrees of freedom in choosing renormalization conditions, or fitting schemes of the low-energy constants. By exploiting this freedom near the exceptional cutoffs, we are able to remove the said correlations. A much-mitigated cutoff variation of the phase shifts, which is acceptable to the power counting, is thus obtained.