Vitrimers are promising reprocessable materials. To tune their properties, microphase separated block copolymers as backbones play an essential role in the thermal and mechanical properties of the resulting nanostructured networks. In this study, various narrow disperse di-and triblock copolymers containing a hydroxyethyl methacrylate block and, for comparison, random copolymers of the same comonomers are synthesized in a controlled manner by photoiniferter reversible addition-fragmentation chain transfer polymerization. Subsequently, the copolymers are modified by acetoacetate groups and cross-linked with diamines. After curing, the di-and triblock copolymer-based vitrimers exhibit excellent thermal and mechanical properties compared to random ones; moreover, their characteristic properties can be adjusted by different types and amounts of diamines. As the transamination reaction is a thermoreversible exchange reaction, the resulting vitrimers are reprocessable and therefore are recyclable materials. The combining of two of these classes of soft materials, namely vitrimers and block copolymers, leads to materials with a broad spectrum of adjustable mechanical properties for various applications with an improved end-of-life management, when compared to permanently crosslinked thermosets.