For an engineered thick tissue construct to be alive and sustainable, it should be perfusable with respect to nutrients and oxygen. Embedded printing and then removing sacrificial inks in a cross-linkable yield-stress hydrogel matrix bath can serve as a valuable tool for fabricating perfusable tissue constructs. The objective of this study is to investigate the printability of sacrificial inks and the creation of perfusable channels in a cross-linkable yield-stress hydrogel matrix during embedded printing. Pluronic F-127, methylcellulose, and polyvinyl alcohol are selected as three representative sacrificial inks for their different physical and rheological properties. Their printability and removability performances have been evaluated during embedded printing in a gelatin microgel-based gelatin composite matrix bath, which is a cross-linkable yield-stress bath. The ink printability during embedded printing is different from that during printing in air due to the constraining effect of the matrix bath. Sacrificial inks with a shear-thinning property are capable of printing channels with a broad range of filaments by simply tuning the extrusion pressure. Bi-directional diffusion may happen between the sacrificial ink and matrix bath, which affects the sacrificial ink removal process and final channel diameter. As such, sacrificial inks with a low diffusion coefficient for gelatin precursor are desirable to minimize the diffusion from the gelatin precursor solution to minimize the post-printing channel diameter variation. For feasibility demonstration, a multi-channel perfusable alveolar mimic has been successfully designed, printed, and evaluated. The study results in the knowledge of the channel diameter controllability and sacrificial ink removability during embedded printing.