To protect the intellectual property of well-trained deep neural networks (DNNs), black-box DNN watermarks, which are embedded into the prediction behavior of DNN models on a set of specially-crafted samples, have gained increasing popularity in both academy and industry. Watermark robustness is usually implemented against attackers who steal the protected model and obfuscate its parameters for watermark removal. Recent studies empirically prove the robustness of most black-box watermarking schemes against known removal attempts. In this paper, we propose a novel Model Inversion-based Removal Attack (\textsc{Mira}), which is watermark-agnostic and effective against most of mainstream black-box DNN watermarking schemes. In general, our attack pipeline exploits the internals of the protected model to recover and unlearn the watermark message. We further design target class detection and recovered sample splitting algorithms to reduce the utility loss caused by \textsc{Mira} and achieve data-free watermark removal on half of the watermarking schemes. We conduct comprehensive evaluation of \textsc{Mira} against ten mainstream black-box watermarks on three benchmark datasets and DNN architectures. Compared with six baseline removal attacks, \textsc{Mira} achieves strong watermark removal effects on the covered watermarks, preserving at least $90\%$ of the stolen model utility, under more relaxed or even no assumptions on the dataset availability.