This paper presents a new $\tau $-lepton reconstruction and identification procedure at the ATLAS detector at the Large Hadron Collider, which leads to significantly improved performance in the case of physics processes where a highly boosted pair of $\tau $-leptons is produced and one $\tau $-lepton decays into a muon and two neutrinos ($\tau _\mathrm {\mu }$), and the other decays into hadrons and one neutrino ($\tau _\textrm{had}$). By removing the muon information from the signals used for reconstruction and identification of the $\tau _\textrm{had}$ candidate in the boosted pair, the efficiency is raised to the level expected for an isolated $\tau _\textrm{had}$. The new procedure is validated by selecting a sample of highly boosted $Z\rightarrow \tau _\mathrm {\mu }\tau _\textrm{had}$ candidates from the data sample of 140 $\textrm{fb}^{-1}$ of proton–proton collisions at 13 TeV recorded with the ATLAS detector. Good agreement is found between data and simulation predictions in both the $Z\rightarrow \tau _\mathrm {\mu }\tau _\textrm{had}$ signal region and in a background validation region. The results presented in this paper demonstrate the effectiveness of the $\tau _\textrm{had}$ reconstruction with muon removal in enhancing the signal sensitivity of the boosted $\tau _\mathrm {\mu }\tau _\textrm{had}$ channel at the ATLAS detector.