Transplantable ready-made microvessels have therapeutic potential for tissue regeneration and cell replacement therapy. Inspired by the natural rapid angiogenic sprouting of microvessels in vivo, engineered injectable 3D microvessel networks are created using thermoplastic elastomer (TPE) microfluidic devices. The TPE material used here is flexible, optically transparent, and can be robustly yet reversibly bonded to a variety of plastic substrates, making it a versatile choice for microfluidic device fabrication because it overcomes the weak self-adhesion properties and limited manufacturing options of poly(dimethylsiloxane) (PDMS). By leveraging the reversible bonding characteristics of TPE material templates, we present their utility as an organ-on-a-chip platform for forming and handling microvessel networks, and demonstrate their potential for animal-free tissue generation and transplantation in clinical applications. We first show that TPE-based devices have nearly 6-fold higher bonding strength during the cell culture step compared to PDMS-based devices while simultaneously maintaining a full reversible bond to (PS) culture plates, which are widely used for biological cell studies. We also demonstrate the successful generation of perfusable and interconnected 3D microvessel networks using TPE-PS microfluidic devices on both single and multi-vessel loading platforms. Importantly, after removing the TPE slab, microvessel networks remain intact on the PS substrate without any structural damage and can be effectively harvested following gel digestion. The TPE-based organ-on-a-chip platform offers substantial advantages by facilitating the harvesting procedure and maintaining the integrity of microfluidic-engineered microvessels for transplant. To the best of our knowledge, our TPE-based reversible bonding approach marks the first confirmation of successful retrieval of organ-specific vessel segments from the reversibly-bonded TPE microfluidic platform. We anticipate that the method will find applications in organ-on-a-chip and microphysiological system research, particularly in tissue analysis and vessel engraftment, where flexible and reversible bonding can be utilized.