Abstract Printing human tissues and organs replete with biomimetic vascular networks is of growing interest. While it is possible to embed perfusable channels within acellular and densely cellular matrices, they do not currently possess the biomimetic architectures found in native vessels. Here, coaxial sacrificial writing into functional tissues (co‐SWIFT) is developed, an embedded bioprinting method capable of generating hierarchically branching, multilayered vascular networks within both granular hydrogel and densely cellular matrices. Coaxial printheads are designed with an extended core–shell configuration to facilitate robust core–core and shell–shell interconnections between printed branching vessels during embedded bioprinting. Using optimized core–shell ink combinations, biomimetic vessels composed of a smooth muscle cell‐laden shell that surrounds perfusable lumens are coaxially printed into granular matrices composed of: 1) transparent alginate microparticles, 2) sacrificial microparticle‐laden collagen, or 3) cardiac spheroids derived from human induced pluripotent stem cells. Biomimetic blood vessels that exhibit good barrier function are produced by seeding these interconnected lumens with a confluent layer of endothelial cells. Importantly, it is found that co‐SWIFT cardiac tissues mature under perfusion, beat synchronously, and exhibit a cardio‐effective drug response in vitro. This advance opens new avenues for the scalable biomanufacturing of vascularized organ‐specific tissues for drug testing, disease modeling, and therapeutic use.